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School of General Relativity, Astrophysics and Cosmology

→ Europe/Warsaw
Lecture hall: 0.06 (Warsaw) (Warszawa/Chęciny)

Lecture hall: 0.06 (Warsaw)

Warszawa/Chęciny

Faculty of Physics, University of Warsaw, Pasteura 5, Warszawa European Centre for Geological Education, Korzecko 1C, Chęciny
Jerzy Lewandowski (University of Warsaw), Adam Szereszewski (University of Warsaw)
Description

The first edition of the School of General Relativity, Astrophysics and Cosmology is organised by the University of Warsaw, Jagiellonian University and the Polish Society on Relativity. Our school is dedicated to PhD students and postdocs conducting research in general relativity theory. The summer school will be divided into two parts: the first will be held at the Faculty of Physics, University of Warsaw from July 24-29, and the second at the European Center for Geological Education in Chęciny from July 31-August 4 - bus transportation from Warsaw to Chęciny will be provided for all the participants. Participants will have opportunity to present their posters.
If you are unable to find funding for accommodation during the first part of the School you may apply for financial assistance during registration.

The School is aimed to PhD students and academic employee who obtained a doctoral degree no earlier than 7 years ago.

 

Lectures (Warsaw):

Abhay Ashtekar:   Gravitational waves: interplay between mathematical foundations and observations

Maciej Dunajski:   Twistor methods in General Relativity 

Rod Gover:   Conformal and related techniques for applications in GR

Ruth Gregory:   On the Nature and Mathematics of Black Holes

Piotr Jaranowski:   Post-Newtonian General Relativity and Gravitational Waves

Adam Pound:   Self-force theory and the gravitational two-body problem

 

Lectures (Chęciny):

Julian Adamek:   Relativistic Simulations for Cosmology

Vladimir Karas:   Relativistic effects in spectra and polarization from black hole accretion disks

Mikołaj Korzyński:   Redshift drift, position drift and parallax in general relativity

Patryk Mach:    Matter around black holes - self-gravitating systems

Olivier Sarbach:   Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole

Marek Szczepańczyk:   The quest to detect gravitational waves

Organizing Committee: 
Lars Andersson (Max-Planck-Institut für Gravitationsphysik: Potsdam), Bartłomiej Bąk (University of Warsaw), Piotr Chruściel (University of Vienna), Jerzy Lewandowski  (University of Warsaw), Patryk Mach (Jagiellonian University), Adam Szereszewski  (University of Warsaw), Sebastian Szybka (Jagiellonian University).

Local Organizers: 
Eryk Buk,  Joanna Ciesielska,  Maciej Kolanowski, Marta Kowol, Maciej Ossowski,  Anna Pawelec,  Krystyna Wójcik

GRSch2023_Warsaw_schedule.pdf
Lectures.pdf
MAP-CAMPUS-OCHOTA.pdf
Restaurants.pdf
Contact
  • Monday, 24 July
    • 09:00 → 11:00
      On the Nature and Mathematics of Black Holes Room 0.06 (Faculty of Physics, University of Warsaw)

      Room 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

      Convener: Ruth Gregory (King’s College London)
      • 09:00
        On the Nature and Mathematics of Black Holes, part I 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

        Speaker: Ruth Gregory (King’s College London)
      • 10:00
        On the Nature and Mathematics of Black Holes, part II 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

        Speaker: Ruth Gregory (King’s College London)
    • 11:00 → 11:20
      Coffee Break 20m Corridor next to lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Corridor next to lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warszawa
    • 11:20 → 13:20
      Self-force theory and the gravitational two-body problem Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      Gravitational self-force theory is the principal method of modelling compact binaries with small mass ratios. In these lectures, I describe the mathematical foundations of self-force theory, its place in the gravitational two-body problem, and its applications in gravitational-wave astronomy.

      Convener: Adam Pound (University of Southampton)
      Warsaw_L1.pdf
      Warsaw_L2.pdf
      Warsaw_L3.pdf
      Warsaw_L4.pdf
      • 11:20
        Self-force theory and the gravitational two-body problem, part I 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Gravitational self-force theory is the principal method of modelling compact binaries with small mass ratios. In these lectures, I describe the mathematical foundations of self-force theory, its place in the gravitational two-body problem, and its applications in gravitational-wave astronomy.

        Speaker: Adam Pound (University of Southampton)
      • 12:20
        Self-force theory and the gravitational two-body problem, part II 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Gravitational self-force theory is the principal method of modelling compact binaries with small mass ratios. In these lectures, I describe the mathematical foundations of self-force theory, its place in the gravitational two-body problem, and its applications in gravitational-wave astronomy.

        Speaker: Adam Pound (University of Southampton)
    • 13:20 → 15:00
      Lunch Break 1h 40m
    • 15:00 → 17:00
      Twistor methods in General Relativity Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

      This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

      Convener: Maciej Dunajski (University of Cambridge)
      • 15:00
        Twistor methods in General Relativity, part I 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

        This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

        Speaker: Maciej Dunajski (University of Cambridge)
      • 16:00
        Twistor methods in General Relativity, part II 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

        This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

        Speaker: Maciej Dunajski (University of Cambridge)
  • Tuesday, 25 July
    • 09:00 → 11:00
      On the Nature and Mathematics of Black Holes Room 0.06 (Faculty of Physics, University of Warsaw)

      Room 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

      Convener: Ruth Gregory (King’s College London)
      • 09:00
        On the Nature and Mathematics of Black Holes, part III 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

        Speaker: Ruth Gregory (King’s College London)
      • 10:00
        On the Nature and Mathematics of Black Holes, part IV 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

        Speaker: Ruth Gregory (King’s College London)
    • 11:00 → 11:20
      Coffee Break 20m Corridor next to lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Corridor next to lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw
    • 11:20 → 13:20
      Self-force theory and the gravitational two-body problem Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      Gravitational self-force theory is the principal method of modelling compact binaries with small mass ratios. In these lectures, I describe the mathematical foundations of self-force theory, its place in the gravitational two-body problem, and its applications in gravitational-wave astronomy.

      Convener: Adam Pound (University of Southampton)
      Warsaw_L1.pdf
      Warsaw_L2.pdf
      Warsaw_L3.pdf
      Warsaw_L4.pdf
      • 11:20
        Self-force theory and the gravitational two-body problem, part III 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Gravitational self-force theory is the principal method of modelling compact binaries with small mass ratios. In these lectures, I describe the mathematical foundations of self-force theory, its place in the gravitational two-body problem, and its applications in gravitational-wave astronomy.

        Speaker: Adam Pound (University of Southampton)
      • 12:20
        Self-force theory and the gravitational two-body problem, part IV 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Gravitational self-force theory is the principal method of modelling compact binaries with small mass ratios. In these lectures, I describe the mathematical foundations of self-force theory, its place in the gravitational two-body problem, and its applications in gravitational-wave astronomy.

        Speaker: Adam Pound (University of Southampton)
    • 13:20 → 15:00
      Lunch Break 1h 40m
    • 15:00 → 17:00
      Twistor methods in General Relativity Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

      This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

      Convener: Maciej Dunajski (University of Cambridge)
      • 15:00
        Twistor methods in General Relativity, part III 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

        This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

        Speaker: Maciej Dunajski (University of Cambridge)
      • 16:00
        Twistor methods in General Relativity, part IV 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

        This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

        Speaker: Maciej Dunajski (University of Cambridge)
  • Wednesday, 26 July
    • 09:00 → 11:00
      On the Nature and Mathematics of Black Holes Room 0.06 (Faculty of Physics, University of Warsaw)

      Room 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

      Convener: Ruth Gregory (King’s College London)
      • 09:00
        On the Nature and Mathematics of Black Holes, part V 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

        Speaker: Ruth Gregory (King’s College London)
      • 10:00
        On the Nature and Mathematics of Black Holes, part VI 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        In this short course we will explore various of the fascinating aspects of black holes in four, and more, dimensions. We start with a review of a general Birkhoff theorem in arbitrary dimension and cosmological constant, then discuss the types of black objects that are possible. We will discuss no hair theorems and black hole perturbations, and the fascinating recent developments in black hole thermodynamics. We will then talk about black holes in cosmology, time dependence and finally link to the standard model via instantons and vacuum decay.

        Speaker: Ruth Gregory (King’s College London)
    • 11:00 → 11:20
      Coffee break 20m Corridor next to lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Corridor next to lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw
    • 13:20 → 14:20
      Lunch break 1h
    • 14:20 → 15:00
      Poster session
    • 15:00 → 17:00
      Gravitational waves: interplay between mathematical foundations and observations Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

      Convener: Abhay Ashtekar (The Pennsylvania State University)
      FullCourse-Reduced.pdf
      • 15:00
        Gravitational waves: interplay between mathematical foundations and observations, part I 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

        Speaker: Abhay Ashtekar (The Pennsylvania State University)
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
      • 16:00
        Gravitational waves: interplay between mathematical foundations and observations, part II 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

        Speaker: Abhay Ashtekar (The Pennsylvania State University)
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
  • Thursday, 27 July
    • 11:00 → 11:20
      Coffee break 20m Corridor next to lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Corridor next to lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw
    • 11:20 → 13:20
      Twistor methods in General Relativity Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

      This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

      Convener: Maciej Dunajski (University of Cambridge)
      • 11:20
        Twistor methods in General Relativity, part V 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

        This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

        Speaker: Maciej Dunajski (University of Cambridge)
      • 12:20
        Twistor methods in General Relativity, part VI 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Twistor theory was originally proposed by Roger Penrose as a new geometric framework for physics that aims to unify general relativity and quantum mechanics. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three–fold, the twistor space.

        This mini course will provide an elementary introduction to twistor theory leading to applications of twistor methods to gravitational instantons.

        Speaker: Maciej Dunajski (University of Cambridge)
    • 13:20 → 15:00
      Lunch break 1h 40m
    • 15:00 → 17:00
      Post-Newtonian General Relativity and Gravitational Waves Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw

      Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

      Convener: Piotr Jaranowski (University of Bialystok)
      GRSchool1.pdf
      GRSchool2.pdf
      GRSchool3.pdf
      GRSchool4.pdf
      • 15:00
        Post-Newtonian General Relativity and Gravitational Waves, part I 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

        Speaker: Piotr Jaranowski (University of Bialystok)
      • 16:00
        Post-Newtonian General Relativity and Gravitational Waves, part II 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

        Speaker: Piotr Jaranowski (University of Bialystok)
  • Friday, 28 July
    • 11:00 → 11:20
      Coffee break 20m Corridor next to lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Corridor next to lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw
    • 11:20 → 13:20
      Post-Newtonian General Relativity and Gravitational Waves Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5. Warsaw

      Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

      Convener: Piotr Jaranowski (University of Bialystok)
      GRSchool1.pdf
      GRSchool2.pdf
      GRSchool3.pdf
      GRSchool4.pdf
      • 11:20
        Post-Newtonian General Relativity and Gravitational Waves, part III 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

        Speaker: Piotr Jaranowski (University of Bialystok)
      • 12:20
        Post-Newtonian General Relativity and Gravitational Waves, part IV 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

        Speaker: Piotr Jaranowski (University of Bialystok)
    • 13:20 → 15:00
      Lunch break 1h 40m
    • 15:00 → 17:00
      Gravitational waves: interplay between mathematical foundations and observations Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5. Warsaw

      This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

      Convener: Abhay Ashtekar (The Pennsylvania State University)
      FullCourse-Reduced.pdf
      • 15:00
        Gravitational waves: interplay between mathematical foundations and observations, part III 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

        Speaker: Abhay Ashtekar (The Pennsylvania State University)
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
      • 16:00
        Gravitational waves: interplay between mathematical foundations and observations, part IV 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

        Speaker: Abhay Ashtekar (The Pennsylvania State University)
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
  • Saturday, 29 July
    • 10:00 → 11:00
      Post-Newtonian General Relativity and Gravitational Waves Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5. Warsaw

      Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

      Convener: Piotr Jaranowski (University of Bialystok)
      GRSchool1.pdf
      GRSchool2.pdf
      GRSchool3.pdf
      GRSchool4.pdf
      • 10:00
        Post-Newtonian General Relativity and Gravitational Waves, part V 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

        Speaker: Piotr Jaranowski (University of Bialystok)
    • 11:00 → 11:20
      Coffee break 20m Corridor next to lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Corridor next to lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5, Warsaw
    • 11:20 → 12:20
      Post-Newtonian General Relativity and Gravitational Waves Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5. Warsaw

      Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

      Convener: Piotr Jaranowski (University of Bialystok)
      GRSchool1.pdf
      GRSchool2.pdf
      GRSchool3.pdf
      GRSchool4.pdf
      • 11:20
        Post-Newtonian General Relativity and Gravitational Waves, part VI 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        Higher-order post-Newtonian (PN) corrections to the equations of motion of compact binary systems composed of black holes or neutron stars are fundamental to the development and success of gravitational-wave astronomy. In the series of lectures, I will present the application of the ADM Hamiltonian formalism of general relativity to deriving equations of motion of compact binary systems within the perturbative PN scheme. Both conservative and dissipative (related to the emission of gravitational waves) effects in the dynamics will be considered.

        Speaker: Piotr Jaranowski (University of Bialystok)
    • 12:20 → 15:00
      Lunch break 2h 40m
    • 15:00 → 17:00
      Gravitational waves: interplay between mathematical foundations and observations Lecture hall 0.06 (Faculty of Physics, University of Warsaw)

      Lecture hall 0.06

      Faculty of Physics, University of Warsaw

      Pasteura 5. Warsaw

      This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

      Convener: Abhay Ashtekar (The Pennsylvania State University)
      FullCourse-Reduced.pdf
      • 15:00
        Gravitational waves: interplay between mathematical foundations and observations, part V 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

        Speaker: Abhay Ashtekar (The Pennsylvania State University)
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
      • 16:00
        Gravitational waves: interplay between mathematical foundations and observations, part VI 45m Lecture hall 0.06

        Lecture hall 0.06

        Faculty of Physics, University of Warsaw

        Pasteura 5, Warsaw

        This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

        Speaker: Abhay Ashtekar (The Pennsylvania State University)
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
        • Gravitational waves: interplay between mathematical foundations and observations 1h

          This mini-course will have two parts. The first will be devoted to conceptual and mathematical issues associated with gravitational waves in full nonlinear general relativity. The second part will illustrate the use of these results as a diagnostic tool to improve waveform models. These discussions will complement those on approximation and numerical methods.

          Speaker: Abhay Ashtekar
  • Sunday, 30 July
    • 16:30 → 19:15
      Travel to Chęciny 2h 45m
  • Monday, 31 July
    • 09:00 → 10:00
      Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole

      These lectures start with a discussion of some of the properties of the most important black hole solution in general relativity and relativistic astrophysics: the Kerr black hole. In particular, the notions of static and stationary observers, ergospheres, horizons, causal structure and the motion of free-falling massive and massless particles will be reviewed. Next, some tools are introduced to understand the geometry of the cotangent bundle associated with a (generic) curved spacetime (M,g). Based on these tools, a manifestly covariant theory is derived describing a relativistic Vlasov gas, that is, a gas consisting of collisionless particles propagating in (M,g). In the final part of the lectures, this theory is applied to the study of the dynamics of a Vlasov gas consisting of particles which follow spatially bound timelike geodesics in the exterior of a Kerr black hole. To this purpose, generalized action-angle variables are introduced in which the geodesic flow simplify considerably and the relativistic Vlasov equation can be solved analytically. Based on this representation, it is shown that - even though it is collisionless - the gas undergoes a relaxation process and settles down to a stationary, axisymmetric configuration. The underlying mechanism for this effect, which is due to phase mixing, will be explained.

      Convener: Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
    • 10:00 → 11:00
      The quest to detect gravitational waves

      Gravitational-Wave Astrophysics, a newly established field, is an exciting frontier for scientific discovery. It opens up possibilities to investigate phenomena that were previously inaccessible through time-domain astronomy. Notably, among the nearly hundred gravitational-wave detections, the first binary black hole merger and an intermediate-mass black hole have been remarkable observations that challenged our understanding of the Universe. The fourth observing run of LIGO, Virgo, and KAGRA presents great opportunities for discoveries. During the course, I will review a range of topics about the Gravitational-Wave Astrophysics. I will outline the gravitational-wave detectors, their operation, noise sources, and future designs. During the lectures, I will give a brief overview of the gravitational-wave data analysis and focus on the model-independent methods. I will discuss the compact binary sources detected centering around the exceptional events. Finally, I will talk about the current observing run of the gravitational-wave detectors.

      Convener: Marek Szczepańczyk
      Szczepanczyk_Checiny_2023_lectures.pdf
    • 11:00 → 11:20
      Coffee break 20m
    • 11:20 → 12:20
      Relativistic Simulations for Cosmology

      Cosmological N-body simulations are one of the most versatile tools for studying the evolution of large-scale structure in the Universe. While the Newtonian limit of general relativity can be used for most purposes within the basic LCDM model, the true nature of the dark components (dark matter and dark energy) is unknown and may ultimately require a relativistic description. Also the neutrinos from the standard model are relativistic for most of the cosmic history if they have a mass within the range allowed by cosmological and laboratory constraints. In this course I will introduce a framework for relativistic N-body simulations that can treat any relativistic degrees of freedom self-consistently. Furthermore, I will discuss the important aspect of how the simulation data are mapped to observables by constructing the past light cone of an observation event. A metric-based approach is presented that is also suitable for treating a wide range of models beyond LCDM.

      Suggested reading: * Chapters 1 and 2 of Baumgarte & Shapiro, "NUMERICAL RELATIVITY - Solving Einstein's Equations on the Computer" * Sections 2 and 3 of "Relativistic N-body simulations with massive neutrinos" (Adamek, Durrer & Kunz, arXiv:1707.06938)

      Convener: Julian Adamek (University of Zurich)
    • 12:20 → 13:20
      Redshift drift, position drift and parallax in general relativity

      I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. With the recent advancements in astrometry, the drifts of distant sources are likely to become important observables in cosmology in the near future. In my lecture I will present the derivation of exact relativistic formulas for the drifts. I will show how the drifts may be expressed in terms of the kinematical variables characterizing the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completly general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences and their possible applications to the gravitational lensing theory, cosmology and pulsar timing. Building on the same formalism I will also consider the trigonometric parallax effect in general relativity, and show how we can measure the mass density along the line of sight by comparing the parallax distance and the angular diameter distance to a single source.

      Literature:
       "Optical drift effects in general relativity", M. Korzyński, J. Kopiński, Journal of Cosmology and Astroparticle Physics 03 (2018) 012
      "Geometric optics in general relativity using bilocal operators", M. Grasso, M. Korzyński, J. Serbenta, Phys. Rev. D 99 (2019) no.6, 064038
      "Geometric optics in relativistic cosmology: new formulation and a new observable", M. Korzyński, E. Villa, Phys. Rev. D 101 (2020) no.6, 063506

      Prerequisites:
      Basic general relativity: worldlines, null and timelike geodesics, parallel transport, curvature tensor, Einstein equations
      Basic cosmology: Friedmann equations, cosmological distances, redshift
      Somewhat more advanced topics in general relativity: geodesic deviation equation, optical Sachs equations (recommended but not necessary, I will introduce this material during the course)

      Convener: Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
    • 13:20 → 15:00
      Lunch break 1h 40m
    • 15:00 → 16:00
      Matter around black holes - self-gravitating systems

      Matter around black holes is usually modeled neglecting its self-gravity, i.e., assuming a fixed background metric. In these lectures I will focus on the opposite case, in which the self-gravity of matter is taken into account. Simple general-relativistic systems in which the effects of self-gravity can be studied include axially symmetric configurations - stationary disks (or tori) around black holes - or spherically symmetric steady accretion flows. I will consider mostly hydrodynamical or magentohydrodynamical models. The interplay between the structure of spacetime affected by the self-gravity of matter and the motion of matter around black holes leads to several interesting phenomena, which I will shortly discuss: bifurcations of solutions, occurrence of various ergoregions, changes in the phase-space of geodesic orbits.

      Convener: Patryk Mach (Jagiellonian University)
    • 16:00 → 17:00
      Redshift drift, position drift and parallax in general relativity

      I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. With the recent advancements in astrometry, the drifts of distant sources are likely to become important observables in cosmology in the near future. In my lecture I will present the derivation of exact relativistic formulas for the drifts. I will show how the drifts may be expressed in terms of the kinematical variables characterizing the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completly general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences and their possible applications to the gravitational lensing theory, cosmology and pulsar timing. Building on the same formalism I will also consider the trigonometric parallax effect in general relativity, and show how we can measure the mass density along the line of sight by comparing the parallax distance and the angular diameter distance to a single source.

      Literature:
       "Optical drift effects in general relativity", M. Korzyński, J. Kopiński, Journal of Cosmology and Astroparticle Physics 03 (2018) 012
      "Geometric optics in general relativity using bilocal operators", M. Grasso, M. Korzyński, J. Serbenta, Phys. Rev. D 99 (2019) no.6, 064038
      "Geometric optics in relativistic cosmology: new formulation and a new observable", M. Korzyński, E. Villa, Phys. Rev. D 101 (2020) no.6, 063506

      Prerequisites:
      Basic general relativity: worldlines, null and timelike geodesics, parallel transport, curvature tensor, Einstein equations
      Basic cosmology: Friedmann equations, cosmological distances, redshift
      Somewhat more advanced topics in general relativity: geodesic deviation equation, optical Sachs equations (recommended but not necessary, I will introduce this material during the course)

      Convener: Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
    • 19:00 → 21:00
      Dinner 2h
  • Tuesday, 1 August
    • 09:00 → 10:00
      Relativistic Simulations for Cosmology

      Cosmological N-body simulations are one of the most versatile tools for studying the evolution of large-scale structure in the Universe. While the Newtonian limit of general relativity can be used for most purposes within the basic LCDM model, the true nature of the dark components (dark matter and dark energy) is unknown and may ultimately require a relativistic description. Also the neutrinos from the standard model are relativistic for most of the cosmic history if they have a mass within the range allowed by cosmological and laboratory constraints. In this course I will introduce a framework for relativistic N-body simulations that can treat any relativistic degrees of freedom self-consistently. Furthermore, I will discuss the important aspect of how the simulation data are mapped to observables by constructing the past light cone of an observation event. A metric-based approach is presented that is also suitable for treating a wide range of models beyond LCDM.

      Suggested reading: * Chapters 1 and 2 of Baumgarte & Shapiro, "NUMERICAL RELATIVITY - Solving Einstein's Equations on the Computer" * Sections 2 and 3 of "Relativistic N-body simulations with massive neutrinos" (Adamek, Durrer & Kunz, arXiv:1707.06938)

      Convener: Julian Adamek (University of Zurich)
    • 10:00 → 11:00
      Redshift drift, position drift and parallax in general relativity

      I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. With the recent advancements in astrometry, the drifts of distant sources are likely to become important observables in cosmology in the near future. In my lecture I will present the derivation of exact relativistic formulas for the drifts. I will show how the drifts may be expressed in terms of the kinematical variables characterizing the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completly general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences and their possible applications to the gravitational lensing theory, cosmology and pulsar timing. Building on the same formalism I will also consider the trigonometric parallax effect in general relativity, and show how we can measure the mass density along the line of sight by comparing the parallax distance and the angular diameter distance to a single source.

      Literature:
       "Optical drift effects in general relativity", M. Korzyński, J. Kopiński, Journal of Cosmology and Astroparticle Physics 03 (2018) 012
      "Geometric optics in general relativity using bilocal operators", M. Grasso, M. Korzyński, J. Serbenta, Phys. Rev. D 99 (2019) no.6, 064038
      "Geometric optics in relativistic cosmology: new formulation and a new observable", M. Korzyński, E. Villa, Phys. Rev. D 101 (2020) no.6, 063506

      Prerequisites:
      Basic general relativity: worldlines, null and timelike geodesics, parallel transport, curvature tensor, Einstein equations
      Basic cosmology: Friedmann equations, cosmological distances, redshift
      Somewhat more advanced topics in general relativity: geodesic deviation equation, optical Sachs equations (recommended but not necessary, I will introduce this material during the course)

      Convener: Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
    • 11:00 → 11:20
      Coffee break 20m
    • 11:20 → 12:20
      Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole

      These lectures start with a discussion of some of the properties of the most important black hole solution in general relativity and relativistic astrophysics: the Kerr black hole. In particular, the notions of static and stationary observers, ergospheres, horizons, causal structure and the motion of free-falling massive and massless particles will be reviewed. Next, some tools are introduced to understand the geometry of the cotangent bundle associated with a (generic) curved spacetime (M,g). Based on these tools, a manifestly covariant theory is derived describing a relativistic Vlasov gas, that is, a gas consisting of collisionless particles propagating in (M,g). In the final part of the lectures, this theory is applied to the study of the dynamics of a Vlasov gas consisting of particles which follow spatially bound timelike geodesics in the exterior of a Kerr black hole. To this purpose, generalized action-angle variables are introduced in which the geodesic flow simplify considerably and the relativistic Vlasov equation can be solved analytically. Based on this representation, it is shown that - even though it is collisionless - the gas undergoes a relaxation process and settles down to a stationary, axisymmetric configuration. The underlying mechanism for this effect, which is due to phase mixing, will be explained.

      Convener: Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
    • 12:20 → 13:20
      The quest to detect gravitational waves

      Gravitational-Wave Astrophysics, a newly established field, is an exciting frontier for scientific discovery. It opens up possibilities to investigate phenomena that were previously inaccessible through time-domain astronomy. Notably, among the nearly hundred gravitational-wave detections, the first binary black hole merger and an intermediate-mass black hole have been remarkable observations that challenged our understanding of the Universe. The fourth observing run of LIGO, Virgo, and KAGRA presents great opportunities for discoveries. During the course, I will review a range of topics about the Gravitational-Wave Astrophysics. I will outline the gravitational-wave detectors, their operation, noise sources, and future designs. During the lectures, I will give a brief overview of the gravitational-wave data analysis and focus on the model-independent methods. I will discuss the compact binary sources detected centering around the exceptional events. Finally, I will talk about the current observing run of the gravitational-wave detectors.

      Convener: Marek Szczepańczyk
      Szczepanczyk_Checiny_2023_lectures.pdf
    • 13:30 → 15:00
      Lunch break 1h 30m
    • 15:00 → 16:00
      Redshift drift, position drift and parallax in general relativity

      I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. With the recent advancements in astrometry, the drifts of distant sources are likely to become important observables in cosmology in the near future. In my lecture I will present the derivation of exact relativistic formulas for the drifts. I will show how the drifts may be expressed in terms of the kinematical variables characterizing the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completly general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences and their possible applications to the gravitational lensing theory, cosmology and pulsar timing. Building on the same formalism I will also consider the trigonometric parallax effect in general relativity, and show how we can measure the mass density along the line of sight by comparing the parallax distance and the angular diameter distance to a single source.

      Literature:
       "Optical drift effects in general relativity", M. Korzyński, J. Kopiński, Journal of Cosmology and Astroparticle Physics 03 (2018) 012
      "Geometric optics in general relativity using bilocal operators", M. Grasso, M. Korzyński, J. Serbenta, Phys. Rev. D 99 (2019) no.6, 064038
      "Geometric optics in relativistic cosmology: new formulation and a new observable", M. Korzyński, E. Villa, Phys. Rev. D 101 (2020) no.6, 063506

      Prerequisites:
      Basic general relativity: worldlines, null and timelike geodesics, parallel transport, curvature tensor, Einstein equations
      Basic cosmology: Friedmann equations, cosmological distances, redshift
      Somewhat more advanced topics in general relativity: geodesic deviation equation, optical Sachs equations (recommended but not necessary, I will introduce this material during the course)

      Convener: Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
    • 16:00 → 17:00
      Matter around black holes - self-gravitating systems

      Matter around black holes is usually modeled neglecting its self-gravity, i.e., assuming a fixed background metric. In these lectures I will focus on the opposite case, in which the self-gravity of matter is taken into account. Simple general-relativistic systems in which the effects of self-gravity can be studied include axially symmetric configurations - stationary disks (or tori) around black holes - or spherically symmetric steady accretion flows. I will consider mostly hydrodynamical or magentohydrodynamical models. The interplay between the structure of spacetime affected by the self-gravity of matter and the motion of matter around black holes leads to several interesting phenomena, which I will shortly discuss: bifurcations of solutions, occurrence of various ergoregions, changes in the phase-space of geodesic orbits.

      Convener: Patryk Mach (Jagiellonian University)
    • 18:30 → 20:00
      Dinner 1h 30m
  • Wednesday, 2 August
    • 09:00 → 10:00
      Relativistic effects in spectra and polarization from black hole accretion disks

      Astrophysical black holes are often characterized by only two parameters, namely, mass and angular momentum. However, cosmic black holes are not completely isolated. Instead, they interact with their gaseous and stellar environment, and so the astrophysically realistic models may require additional information to describe the spacetime metric and to determine the state of the surrounding gaseous environment. We will review a fruitful approach to study variety of electromagnetic signatures from accretion disks in strong gravity regime. Transfer functions can be introduced, pre-computed, and then employed to generate model spectra and to fit them to the electromagnetic signal in X-rays. We have been developing this approach to analyse spectra and light curves and to predict the polarimetric properties. Other groups adopt different schemes which we will briefly outline, too. Models can be finally tested with the current and upcoming observations. Some of recent results challenge the expectations based on standard accretion scenarios.

      Convener: Vladimir Karas (Astronomical Institute, Czech Academy of Sciences)
    • 10:00 → 11:00
      Matter around black holes - self-gravitating systems

      Matter around black holes is usually modeled neglecting its self-gravity, i.e., assuming a fixed background metric. In these lectures I will focus on the opposite case, in which the self-gravity of matter is taken into account. Simple general-relativistic systems in which the effects of self-gravity can be studied include axially symmetric configurations - stationary disks (or tori) around black holes - or spherically symmetric steady accretion flows. I will consider mostly hydrodynamical or magentohydrodynamical models. The interplay between the structure of spacetime affected by the self-gravity of matter and the motion of matter around black holes leads to several interesting phenomena, which I will shortly discuss: bifurcations of solutions, occurrence of various ergoregions, changes in the phase-space of geodesic orbits.

      Convener: Patryk Mach (Jagiellonian University)
    • 11:00 → 11:20
      Coffee break 20m
    • 11:20 → 12:20
      Relativistic Simulations for Cosmology

      Cosmological N-body simulations are one of the most versatile tools for studying the evolution of large-scale structure in the Universe. While the Newtonian limit of general relativity can be used for most purposes within the basic LCDM model, the true nature of the dark components (dark matter and dark energy) is unknown and may ultimately require a relativistic description. Also the neutrinos from the standard model are relativistic for most of the cosmic history if they have a mass within the range allowed by cosmological and laboratory constraints. In this course I will introduce a framework for relativistic N-body simulations that can treat any relativistic degrees of freedom self-consistently. Furthermore, I will discuss the important aspect of how the simulation data are mapped to observables by constructing the past light cone of an observation event. A metric-based approach is presented that is also suitable for treating a wide range of models beyond LCDM.

      Suggested reading: * Chapters 1 and 2 of Baumgarte & Shapiro, "NUMERICAL RELATIVITY - Solving Einstein's Equations on the Computer" * Sections 2 and 3 of "Relativistic N-body simulations with massive neutrinos" (Adamek, Durrer & Kunz, arXiv:1707.06938)

      Convener: Julian Adamek (University of Zurich)
    • 12:20 → 13:20
      Relativistic effects in spectra and polarization from black hole accretion disks

      Astrophysical black holes are often characterized by only two parameters, namely, mass and angular momentum. However, cosmic black holes are not completely isolated. Instead, they interact with their gaseous and stellar environment, and so the astrophysically realistic models may require additional information to describe the spacetime metric and to determine the state of the surrounding gaseous environment. We will review a fruitful approach to study variety of electromagnetic signatures from accretion disks in strong gravity regime. Transfer functions can be introduced, pre-computed, and then employed to generate model spectra and to fit them to the electromagnetic signal in X-rays. We have been developing this approach to analyse spectra and light curves and to predict the polarimetric properties. Other groups adopt different schemes which we will briefly outline, too. Models can be finally tested with the current and upcoming observations. Some of recent results challenge the expectations based on standard accretion scenarios.

      Convener: Vladimir Karas (Astronomical Institute, Czech Academy of Sciences)
    • 13:30 → 15:00
      Lunch break 1h 30m
    • 15:00 → 16:00
      Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole

      These lectures start with a discussion of some of the properties of the most important black hole solution in general relativity and relativistic astrophysics: the Kerr black hole. In particular, the notions of static and stationary observers, ergospheres, horizons, causal structure and the motion of free-falling massive and massless particles will be reviewed. Next, some tools are introduced to understand the geometry of the cotangent bundle associated with a (generic) curved spacetime (M,g). Based on these tools, a manifestly covariant theory is derived describing a relativistic Vlasov gas, that is, a gas consisting of collisionless particles propagating in (M,g). In the final part of the lectures, this theory is applied to the study of the dynamics of a Vlasov gas consisting of particles which follow spatially bound timelike geodesics in the exterior of a Kerr black hole. To this purpose, generalized action-angle variables are introduced in which the geodesic flow simplify considerably and the relativistic Vlasov equation can be solved analytically. Based on this representation, it is shown that - even though it is collisionless - the gas undergoes a relaxation process and settles down to a stationary, axisymmetric configuration. The underlying mechanism for this effect, which is due to phase mixing, will be explained.

      Convener: Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
    • 19:00 → 23:00
      Campfire dinner 1d 4h
  • Thursday, 3 August
    • 09:00 → 10:00
      Matter around black holes - self-gravitating systems

      Matter around black holes is usually modeled neglecting its self-gravity, i.e., assuming a fixed background metric. In these lectures I will focus on the opposite case, in which the self-gravity of matter is taken into account. Simple general-relativistic systems in which the effects of self-gravity can be studied include axially symmetric configurations - stationary disks (or tori) around black holes - or spherically symmetric steady accretion flows. I will consider mostly hydrodynamical or magentohydrodynamical models. The interplay between the structure of spacetime affected by the self-gravity of matter and the motion of matter around black holes leads to several interesting phenomena, which I will shortly discuss: bifurcations of solutions, occurrence of various ergoregions, changes in the phase-space of geodesic orbits.

      Convener: Patryk Mach (Jagiellonian University)
    • 10:00 → 11:00
      Relativistic effects in spectra and polarization from black hole accretion disks

      Astrophysical black holes are often characterized by only two parameters, namely, mass and angular momentum. However, cosmic black holes are not completely isolated. Instead, they interact with their gaseous and stellar environment, and so the astrophysically realistic models may require additional information to describe the spacetime metric and to determine the state of the surrounding gaseous environment. We will review a fruitful approach to study variety of electromagnetic signatures from accretion disks in strong gravity regime. Transfer functions can be introduced, pre-computed, and then employed to generate model spectra and to fit them to the electromagnetic signal in X-rays. We have been developing this approach to analyse spectra and light curves and to predict the polarimetric properties. Other groups adopt different schemes which we will briefly outline, too. Models can be finally tested with the current and upcoming observations. Some of recent results challenge the expectations based on standard accretion scenarios.

      Convener: Vladimir Karas (Astronomical Institute, Czech Academy of Sciences)
    • 11:00 → 11:20
      Coffee break 20m
    • 11:20 → 12:20
      Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole

      These lectures start with a discussion of some of the properties of the most important black hole solution in general relativity and relativistic astrophysics: the Kerr black hole. In particular, the notions of static and stationary observers, ergospheres, horizons, causal structure and the motion of free-falling massive and massless particles will be reviewed. Next, some tools are introduced to understand the geometry of the cotangent bundle associated with a (generic) curved spacetime (M,g). Based on these tools, a manifestly covariant theory is derived describing a relativistic Vlasov gas, that is, a gas consisting of collisionless particles propagating in (M,g). In the final part of the lectures, this theory is applied to the study of the dynamics of a Vlasov gas consisting of particles which follow spatially bound timelike geodesics in the exterior of a Kerr black hole. To this purpose, generalized action-angle variables are introduced in which the geodesic flow simplify considerably and the relativistic Vlasov equation can be solved analytically. Based on this representation, it is shown that - even though it is collisionless - the gas undergoes a relaxation process and settles down to a stationary, axisymmetric configuration. The underlying mechanism for this effect, which is due to phase mixing, will be explained.

      Convener: Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
    • 12:20 → 13:20
      Relativistic effects in spectra and polarization from black hole accretion disks

      Astrophysical black holes are often characterized by only two parameters, namely, mass and angular momentum. However, cosmic black holes are not completely isolated. Instead, they interact with their gaseous and stellar environment, and so the astrophysically realistic models may require additional information to describe the spacetime metric and to determine the state of the surrounding gaseous environment. We will review a fruitful approach to study variety of electromagnetic signatures from accretion disks in strong gravity regime. Transfer functions can be introduced, pre-computed, and then employed to generate model spectra and to fit them to the electromagnetic signal in X-rays. We have been developing this approach to analyse spectra and light curves and to predict the polarimetric properties. Other groups adopt different schemes which we will briefly outline, too. Models can be finally tested with the current and upcoming observations. Some of recent results challenge the expectations based on standard accretion scenarios.

      Convener: Vladimir Karas (Astronomical Institute, Czech Academy of Sciences)
    • 13:30 → 15:00
      Lunch break 1h 30m
    • 15:00 → 16:00
      Relativistic Simulations for Cosmology

      Cosmological N-body simulations are one of the most versatile tools for studying the evolution of large-scale structure in the Universe. While the Newtonian limit of general relativity can be used for most purposes within the basic LCDM model, the true nature of the dark components (dark matter and dark energy) is unknown and may ultimately require a relativistic description. Also the neutrinos from the standard model are relativistic for most of the cosmic history if they have a mass within the range allowed by cosmological and laboratory constraints. In this course I will introduce a framework for relativistic N-body simulations that can treat any relativistic degrees of freedom self-consistently. Furthermore, I will discuss the important aspect of how the simulation data are mapped to observables by constructing the past light cone of an observation event. A metric-based approach is presented that is also suitable for treating a wide range of models beyond LCDM.

      Suggested reading: * Chapters 1 and 2 of Baumgarte & Shapiro, "NUMERICAL RELATIVITY - Solving Einstein's Equations on the Computer" * Sections 2 and 3 of "Relativistic N-body simulations with massive neutrinos" (Adamek, Durrer & Kunz, arXiv:1707.06938)

      Convener: Julian Adamek (University of Zurich)
    • 16:00 → 17:00
      The quest to detect gravitational waves

      Gravitational-Wave Astrophysics, a newly established field, is an exciting frontier for scientific discovery. It opens up possibilities to investigate phenomena that were previously inaccessible through time-domain astronomy. Notably, among the nearly hundred gravitational-wave detections, the first binary black hole merger and an intermediate-mass black hole have been remarkable observations that challenged our understanding of the Universe. The fourth observing run of LIGO, Virgo, and KAGRA presents great opportunities for discoveries. During the course, I will review a range of topics about the Gravitational-Wave Astrophysics. I will outline the gravitational-wave detectors, their operation, noise sources, and future designs. During the lectures, I will give a brief overview of the gravitational-wave data analysis and focus on the model-independent methods. I will discuss the compact binary sources detected centering around the exceptional events. Finally, I will talk about the current observing run of the gravitational-wave detectors.

      Convener: Marek Szczepańczyk
      Szczepanczyk_Checiny_2023_lectures.pdf
    • 18:30 → 20:00
      Dinner 1h 30m
  • Friday, 4 August
    • 09:00 → 10:00
      Relativistic effects in spectra and polarization from black hole accretion disks

      Astrophysical black holes are often characterized by only two parameters, namely, mass and angular momentum. However, cosmic black holes are not completely isolated. Instead, they interact with their gaseous and stellar environment, and so the astrophysically realistic models may require additional information to describe the spacetime metric and to determine the state of the surrounding gaseous environment. We will review a fruitful approach to study variety of electromagnetic signatures from accretion disks in strong gravity regime. Transfer functions can be introduced, pre-computed, and then employed to generate model spectra and to fit them to the electromagnetic signal in X-rays. We have been developing this approach to analyse spectra and light curves and to predict the polarimetric properties. Other groups adopt different schemes which we will briefly outline, too. Models can be finally tested with the current and upcoming observations. Some of recent results challenge the expectations based on standard accretion scenarios.

      Convener: Vladimir Karas (Astronomical Institute, Czech Academy of Sciences)
    • 10:00 → 11:00
      Relativistic Simulations for Cosmology

      Cosmological N-body simulations are one of the most versatile tools for studying the evolution of large-scale structure in the Universe. While the Newtonian limit of general relativity can be used for most purposes within the basic LCDM model, the true nature of the dark components (dark matter and dark energy) is unknown and may ultimately require a relativistic description. Also the neutrinos from the standard model are relativistic for most of the cosmic history if they have a mass within the range allowed by cosmological and laboratory constraints. In this course I will introduce a framework for relativistic N-body simulations that can treat any relativistic degrees of freedom self-consistently. Furthermore, I will discuss the important aspect of how the simulation data are mapped to observables by constructing the past light cone of an observation event. A metric-based approach is presented that is also suitable for treating a wide range of models beyond LCDM.

      Suggested reading: * Chapters 1 and 2 of Baumgarte & Shapiro, "NUMERICAL RELATIVITY - Solving Einstein's Equations on the Computer" * Sections 2 and 3 of "Relativistic N-body simulations with massive neutrinos" (Adamek, Durrer & Kunz, arXiv:1707.06938)

      Convener: Julian Adamek (University of Zurich)
    • 11:00 → 11:20
      Coffee break 20m
    • 11:20 → 12:20
      Matter around black holes - self-gravitating systems

      Matter around black holes is usually modeled neglecting its self-gravity, i.e., assuming a fixed background metric. In these lectures I will focus on the opposite case, in which the self-gravity of matter is taken into account. Simple general-relativistic systems in which the effects of self-gravity can be studied include axially symmetric configurations - stationary disks (or tori) around black holes - or spherically symmetric steady accretion flows. I will consider mostly hydrodynamical or magentohydrodynamical models. The interplay between the structure of spacetime affected by the self-gravity of matter and the motion of matter around black holes leads to several interesting phenomena, which I will shortly discuss: bifurcations of solutions, occurrence of various ergoregions, changes in the phase-space of geodesic orbits.

      Convener: Patryk Mach (Jagiellonian University)
    • 12:20 → 13:20
      Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole

      These lectures start with a discussion of some of the properties of the most important black hole solution in general relativity and relativistic astrophysics: the Kerr black hole. In particular, the notions of static and stationary observers, ergospheres, horizons, causal structure and the motion of free-falling massive and massless particles will be reviewed. Next, some tools are introduced to understand the geometry of the cotangent bundle associated with a (generic) curved spacetime (M,g). Based on these tools, a manifestly covariant theory is derived describing a relativistic Vlasov gas, that is, a gas consisting of collisionless particles propagating in (M,g). In the final part of the lectures, this theory is applied to the study of the dynamics of a Vlasov gas consisting of particles which follow spatially bound timelike geodesics in the exterior of a Kerr black hole. To this purpose, generalized action-angle variables are introduced in which the geodesic flow simplify considerably and the relativistic Vlasov equation can be solved analytically. Based on this representation, it is shown that - even though it is collisionless - the gas undergoes a relaxation process and settles down to a stationary, axisymmetric configuration. The underlying mechanism for this effect, which is due to phase mixing, will be explained.

      Convener: Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
    • 13:30 → 15:00
      Lunch break 1h 30m
    • 15:00 → 16:00
      The quest to detect gravitational waves

      Gravitational-Wave Astrophysics, a newly established field, is an exciting frontier for scientific discovery. It opens up possibilities to investigate phenomena that were previously inaccessible through time-domain astronomy. Notably, among the nearly hundred gravitational-wave detections, the first binary black hole merger and an intermediate-mass black hole have been remarkable observations that challenged our understanding of the Universe. The fourth observing run of LIGO, Virgo, and KAGRA presents great opportunities for discoveries. During the course, I will review a range of topics about the Gravitational-Wave Astrophysics. I will outline the gravitational-wave detectors, their operation, noise sources, and future designs. During the lectures, I will give a brief overview of the gravitational-wave data analysis and focus on the model-independent methods. I will discuss the compact binary sources detected centering around the exceptional events. Finally, I will talk about the current observing run of the gravitational-wave detectors.

      Convener: Marek Szczepańczyk
      Szczepanczyk_Checiny_2023_lectures.pdf
    • 18:30 → 20:00
      Dinner 1h 30m
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