Publication date: May 2018
Abstract:
A test fluid composed of relativistic collisionless neutral particles in
the background of Kerr metric is expected to generate non-isotropic
equilibrium configurations in which the corresponding stress-energy
tensor exhibits pressure and temperature anisotropies. This arises as a
consequence of the constraints placed on single-particle dynamics by
Killing tensor symmetries, leading to a peculiar non-Maxwellian
functional form of the kinetic distribution function describing the
continuum system. Based on this outcome, in this paper the generation of
Kerr-like 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 self-field
correction. The latter one is generated by the uncharged fluid at
equilibrium and satisfies the linearized Einstein equations having the
non-isotropic stress-energy tensor as source term. It is shown that the
resulting self-metric is again of Kerr type, providing a mechanism of
magnification of the background metric tensor and its qualitative
features.
Authors:
Cremaschini, Claudio; Stuchlík, Zdeněk;