Abstract
In previous work, we derived the most general solution of the collisionless Boltzmann equation describing the accretion of a kinetic gas into a Schwarzschild black hole background, and we gave explicit expressions for the corresponding observables (the current density and stress energy-momentum tensor) in terms of certain integrals over the distribution function. In this article, we numerically compute these integrals for the particular case of the steady-state, spherical symmetric accretion flows which, at infinity, are described by an equilibrium distribution function of given temperature. We analyze in detail the behavior of the observables as a function of the temperature and the radial coordinate, comparing our results with the perfect fluid model of Bondi-Michel accretion.
Highlights
During the last few years there has been an increasing interest in the relativistic kinetic theory of gases, originating from the need to consider kinetic gases in extreme situations, either at very high temperatures or in the presence of strong gravitational fields, where the standard Newtonian theory breaks down
This provides a partial explanation for the known fact that the accretion rate for a collisionless gas is low compared to the Bondi-Michel accretion model in the hydrodynamic, isotropic perfect fluid case [11, 12, 13, 14]
In the last part of the article, we provide an explanation for the reason why the kinetic gas ceases to behave as an isotropic perfect fluid in the vicinity of the black hole, even though in our model it fulfills the same conditions as a perfect fluid at infinity
Summary
During the last few years there has been an increasing interest in the relativistic kinetic theory of gases, originating from the need to consider kinetic gases in extreme situations, either at very high temperatures or in the presence of strong gravitational fields, where the standard Newtonian theory breaks down. This provides a partial explanation for the known fact that the accretion rate for a collisionless gas is low compared to the Bondi-Michel accretion model in the hydrodynamic, isotropic perfect fluid case [11, 12, 13, 14].
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