**Publication date:** Jan 2017

**Abstract:**

A new intrinsically-relativistic kinetic mechanism for generation of

nonisotropic relativistic kinetic equilibria in collisionless N-body

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 single-particle

dynamics in prescribed background curved-spacetimes demonstrating

existence of Killing tensors. As an illustration, the particular case of

the Kerr spacetime admitting the so-called 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 Gaussian-like distributions is

provided. It is shown that, due to the Carter constant, these

equilibrium KDFs exhibit an anisotropic phase-space functional

dependence in terms of the single-particle 4-velocity components, giving

rise to corresponding nonisotropic continuum fluid fields. The

qualitative properties of the equilibrium stress-energy 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 stellar-mass

or galactic-center black holes.

**Authors:**

Cremaschini, Claudio; Stuchlík, Zdeněk;