Phase space mixing in the equatorial plane of a Kerr black hole

Abstract

It is shown that a collisionless, relativistic kinetic gas configuration propagating in the equatorial plane of a Kerr black hole undergoes a relaxation process and eventually settles down to a stationary, axisymmetric configuration surrounding the black hole. The underlying mechanism for this relaxation process is due to phase space mixing, which implies that although the one-particle distribution function $f$ satisfying the collisionless Boltzmann equation which describes the microscopic state of the gas is quasi-periodic in time, the associated macroscopic observables computed from averages over $f$ possess well-defined limits as time goes to infinity. The final state of the gas is described by an effective distribution function depending only on constants of motion which can be predicted from the initial distribution function.

arXiv commentImproved version including new plots, the meaning of the main theorem clarified and typos corrected Fig 5, 14 pages

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Cited by in corpus (13)

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• Kerr Geodesics in Terms of Weierstrass Elliptic Functions
• Accretion of the Vlasov gas on Reissner-Nordström black holes
• Accretion of the relativistic Vlasov gas in the equatorial plane of the Kerr black hole
• Accretion of a Vlasov gas on to a black hole from a sphere of finite radius and the role of angular momentum
• Axisymmetric, stationary collisionless gas configurations surrounding black holes
• Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions
• Accretion of a Vlasov gas by a Kerr black hole
• Axisymmetric, stationary collisionless gas clouds trapped in a Newtonian potential
• Mixing in an anharmonic potential well
• Accretion of the degenerate Fermi gas onto a Reissner-Nordström black hole
• Bondi-type accretion onto a Kerr black hole in the kinetic regime
• Spherical accretion of a collisionless kinetic gas into a generic static black hole