Accretion of the relativistic Vlasov gas in the equatorial plane of the Kerr black hole

Abstract

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. The solution is specified by imposing asymptotic boundary conditions: at infinity the gas obeys the Maxwell-Jüttner distribution, restricted to the equatorial plane (both in positions and momenta). In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The rest-mass and energy accretion rates, normalized by the black hole mass and appropriate asymptotic surface densities of the gas, increase with increasing asymptotic temperature. The accretion slows down the rotation of the black hole.

arXiv comment24 pages, 17 figures

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• Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions
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• Accretion of the degenerate Fermi gas onto a Reissner-Nordström black hole
• Spherical accretion of a collisionless kinetic gas into a generic static black hole
• Bondi-type accretion onto a Kerr black hole in the kinetic regime
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• $q$-Equilibrium of Gas in Spacetime of Multi-horizon Black Holes
• A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame