Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole

Understand

We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole.

• To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime.
• The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined.
• Next, we explore the case where the flow is steady-state and spherically symmetric.