Conveners
Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole
- Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole
- Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole
- Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole
- Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
Particle motion and dynamics of a Vlasov gas in the exterior of a Kerr black hole
- Olivier Sarbach (Universidad Michoacana de San Nicolás de Hidalgo)
Description
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.
