**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;