An introduction to the relativistic kinetic theory on curved spacetimes

Acuña-Cárdenas, Rubén O.; Gabarrete, Carlos; Sarbach, Olivier

doi:10.1007/s10714-022-02908-5

Cited by 19 publications

(9 citation statements)

References 109 publications

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“…To extract the physical content of our gas configurations, we compute the most relevant spacetime observables, that is, the particle current density J and the energy-momentum-stress tensor T. In particular, these quantities contain the information about the particle density n, mean particle four-velocity, the energy density ε, heat flow, pressure tensor P ij and kinetic temperature. They are defined as follows (see, for instance, [31,32])…”

Section: Collisionless Boltzmann Equation and Spacetime Observablesmentioning

confidence: 99%

“…(x) = 0, and the remaining orthonormal components of J μ are identically zero. Here, and in the following, R := r sin ϑ refers to the cylindrical radius, and we recall the definitions of the quantities a and b in equation (31). The orthonormal components of the particle current density in equations ( 35) and (36) determine the invariant particle density and fourvelocity of the gas:…”

Section: Spacetime Observablesmentioning

confidence: 99%

“…Throughout this work, we use the signature convention (−, +, +, +) for the spacetime metric and work in geometrized units, such that G N = c = 1. For recent reviews on mathematical results regarding the Einstein-Vlasov system and the geometric structure in the relativistic kinetic theory on curved spacetimes we refer the reader to [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Axisymmetric, stationary collisionless gas configurations surrounding Schwarzschild black holes

Fajardo

Sarbach²

2023

Class. Quantum Grav.

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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 counter-parts in a Newtonian potential are analyzed. Finally, our conﬁgurations are compared to their hydrodynamic analogues, the “polish doughnuts”.

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Section: Collisionless Boltzmann Equation and Spacetime Observablesmentioning

confidence: 99%

Section: Spacetime Observablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Axisymmetric, stationary collisionless gas configurations surrounding Schwarzschild black holes

Fajardo

Sarbach²

2023

Class. Quantum Grav.

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“…Thermodynamic relations characterizing the Maxwell-Jüttner distribution in arbitrary dimensions are given, e.g., in [13], Sec. 3.3.…”

Section: Appendix A: 4 Dimensional Calculationmentioning

confidence: 99%

“…Classic reviews of the general-relativistic kinetic theory can be found e.g. in [5][6][7][8][9][10]; see also [11][12][13] for more recent accounts.…”

Section: Introductionmentioning

confidence: 99%

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

Cieślik¹,

Mach²,

Odrzywołek³

2022

Preprint

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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.

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Phase Space Mixing of a Vlasov Gas in the Exterior of a Kerr Black Hole

Rioseco,

Sarbach

2024

Commun. Math. Phys.

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An introduction to the relativistic kinetic theory on curved spacetimes

Cited by 19 publications

References 109 publications

Axisymmetric, stationary collisionless gas configurations surrounding Schwarzschild black holes

Axisymmetric, stationary collisionless gas configurations surrounding Schwarzschild black holes

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

Phase Space Mixing of a Vlasov Gas in the Exterior of a Kerr Black Hole

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