Axisymmetric, stationary collisionless gas configurations surrounding black holes

TL;DR

This paper models stationary, collisionless gas clouds around black holes using geodesic orbits, deriving macroscopic observables, and comparing relativistic configurations with Newtonian and hydrodynamic analogues.

Contribution

It introduces new models for collisionless gas configurations around black holes, deriving key physical quantities and analyzing their properties and differences from classical models.

Findings

Configurations with finite mass and angular momentum are constructed.

Relativistic gas configurations differ from Newtonian counterparts in key aspects.

Comparison with hydrodynamic 'polish doughnuts' highlights relativistic effects.

Abstract

The properties of a stationary gas cloud surrounding a black hole are discussed, assuming that the gas consists of collisionless, identical massive particles that follow spatially bound geodesic orbits in the Schwarzschild spacetime. Several models for the one-particle distribution function are considered, and the essential formulae that describe the relevant macroscopic observables, like the current density four-vector and the stress-energy-momentum tensor are derived. This is achieved by rewriting these observables as integrals over the constants of motion and by a careful analysis of the range of integration. In particular, we provide configurations with finite total mass and angular momentum. Differences between these configurations and their nonrelativistic counterparts in a Newtonian potential are analyzed. Finally, our configurations are compared to their hydrodynamic analogues, the "polish doughnuts".