Spherical accretion of a collisionless kinetic gas into a generic static black hole

Abstract

We present a nontrivial extension of the problem of spherical accretion of a collisionless kinetic gas into the standard Schwarzschild black hole. This extension consists of replacing the Schwarzschild black hole by generic static and spherically symmetric black hole spacetimes with the aim of studying the effects of either modified gravitational theories beyond Einstein gravity or matter sources coupled to general relativity on the accretion process. This generalization also allows us to investigate the accretion into other types of black hole spacetimes, such as ones inspired by loop quantum gravity and string theory. To do so, we take into account a large class of static and spherically symmetric black holes whose spacetime is asymptotically flat with a positive total mass, has a regular Killing horizon, and satisfies appropriate monotonicity conditions of the metric functions. We provide the most general solution of the collisionless Boltzmann equation on such spacetimes by expressing the one-particle distribution function in terms of suitable symplectic coordinates on the cotangent bundle, and we calculate the relevant observables, such as particle current density and energy-momentum-stress tensor. Specializing to the case where the gas is described by an isotropic ideal fluid at rest at infinity, we compute the mass accretion rate and compression ratio, and we show that the tangential pressure is larger than the radial one at the horizon, indicating that the behavior of a collisionless gas is different from the one of an isotropic perfect fluid. As an example, we apply our generic formulae to two special black hole spacetimes, namely the Reissner-Nordström black hole and a loop quantum corrected black hole. We explore the effects of the free parameters on the observables and accretion rate, and we compare the results with those corresponding to the Schwarzschild black hole.

arXiv comment32 pages with 8 captioned figures; Minor changes to match the published version

References in corpus (40)

• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• Space-Time Structure of Loop Quantum Black Hole
• The Einstein-Vlasov System/Kinetic Theory
• Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
• Analytic solution of the Boltzmann equation in an expanding system
• The geometry of the tangent bundle and the relativistic kinetic theory of gases
• Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole
• Radial accretion flows on static spherically symmetric black holes
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Photon rings as tests for alternative spherically symmetric geometries with thin accretion disks
• Accretion of Dark Matter onto a Moving Schwarzschild Black Hole: An Exact Solution
• Black Holes with Multiple Photon Spheres
• An introduction to the relativistic kinetic theory on curved spacetimes
• The Stability of the Minkowski space for the Einstein-Vlasov system
• Proof of the cosmic no-hair conjecture in the T^3-Gowdy symmetric Einstein-Vlasov setting
• Accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole: Exact solutions
• Spherical steady-state accretion of a relativistic collisionless gas into a Schwarzschild black hole
• Relativistic Kinetic Theory: An Introduction
• The formation of black holes in spherically symmetric gravitational collapse
• 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
• Phase space mixing in the equatorial plane of a 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
• Vlasov versus N-body: the Hénon sphere
• Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
• Black hole formation from a complete regular past for collisionless matter
• Tangent bundle formulation of a charged gas
• Critical collapse in the spherically-symmetric Einstein-Vlasov model
• Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime
• Kinetic gas disks surrounding Schwarzschild black holes
• Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system
• Stable cosmologies with collisionless charged matter
• Observational redshift from general spherically symmetric black holes
• Axisymmetric, stationary collisionless gas configurations surrounding black holes
• A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
• Stationary axisymmetric Einstein-Vlasov bifurcations of the Kerr spacetime
• Oppenheimer-Snyder type collapse for a collisionless gas
• Decay properties for massive Vlasov fields on Schwarzschild spacetime
• Relatively non-degenerate integrated decay estimates for massless Vlasov fields on Schwarzschild spacetimes

Cited by in corpus (2)

• Accretion of a Vlasov gas by a Kerr black hole
• Bondi-type accretion onto a Kerr black hole in the kinetic regime