Conveners
Redshift drift, position drift and parallax in general relativity
- Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
Redshift drift, position drift and parallax in general relativity
- Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
Redshift drift, position drift and parallax in general relativity
- Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
Redshift drift, position drift and parallax in general relativity
- Mikołąj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)
Description
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)
