Magnification effect of Kerr metric by configurations of collisionless particles in nonisotropic kinetic equilibria
Abstract
A test fluid composed of relativistic collisionless neutral particles in the background of Kerr metric is expected to generate nonisotropic equilibrium configurations in which the corresponding stressenergy tensor exhibits pressure and temperature anisotropies. This arises as a consequence of the constraints placed on singleparticle dynamics by Killing tensor symmetries, leading to a peculiar nonMaxwellian functional form of the kinetic distribution function describing the continuum system. Based on this outcome, in this paper the generation of Kerrlike metric by collisionless N body systems of neutral matter orbiting in the field of a rotating black hole is reported. The result is obtained in the framework of covariant kinetic theory by solving the Einstein equations in terms of an analytical perturbative treatment whereby the gravitational field is decomposed as a prescribed background metric tensor described by the Kerr solution plus a selffield correction. The latter one is generated by the uncharged fluid at equilibrium and satisfies the linearized Einstein equations having the nonisotropic stressenergy tensor as source term. It is shown that the resulting selfmetric is again of Kerr type, providing a mechanism of magnification of the background metric tensor and its qualitative features.
 Publication:

European Physical Journal Plus
 Pub Date:
 May 2018
 DOI:
 10.1140/epjp/i2018120439
 Bibcode:
 2018EPJP..133..203C