Carter constant induced mechanism for generation of anisotropic kinetic equilibria in collisionless Nbody systems
Abstract
A new intrinsicallyrelativistic kinetic mechanism for generation of nonisotropic relativistic kinetic equilibria in collisionless Nbody systems is pointed out. The theory is developed in the framework of the covariant Vlasov statistical description. The new effect is based on the constraints placed by the conservation laws of neutral singleparticle dynamics in prescribed background curvedspacetimes demonstrating existence of Killing tensors. As an illustration, the particular case of the Kerr spacetime admitting the socalled Carter constant for the particle geodesic motion is considered. The general functional form of the equilibrium kinetic distribution function (KDF) is determined and an explicit realization in terms of Gaussianlike distributions is provided. It is shown that, due to the Carter constant, these equilibrium KDFs exhibit an anisotropic phasespace functional dependence in terms of the singleparticle 4velocity components, giving rise to corresponding nonisotropic continuum fluid fields. The qualitative properties of the equilibrium stressenergy tensor associated with these systems are discussed, with a particular emphasis on the related occurrence of temperature anisotropy effects. The theory is susceptible of astrophysical applications, including in particular the statistical properties of dark matter (DM) halos around stellarmass or galacticcenter black holes.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2017
 DOI:
 10.1142/S0218271817500018
 arXiv:
 arXiv:2306.10434
 Bibcode:
 2017IJMPD..2650001C
 Keywords:

 Relativistic kinetic theory;
 collosionless neutral matter;
 carter constant;
 killing tensors;
 nonisotropic equilibria;
 04.20.‑q;
 04.20.Jb;
 05.20.Dd;
 05.20.Jj;
 Exact solutions;
 Kinetic theory;
 Statistical mechanics of classical fluids;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 Condensed Matter  Statistical Mechanics
 EPrint:
 14 pages