On black hole solutions in model with anisotropic fluid

TL;DR

This paper explores a family of spherically symmetric solutions in a model with anisotropic fluid, identifying black hole solutions and calculating post-Newtonian parameters relevant for gravitational tests.

Contribution

It introduces a new family of black hole solutions in a model with anisotropic fluid, linking them to known black brane metrics and calculating observational parameters.

Findings

Identified black hole solutions for q=1,2,...

Connected solutions to black brane metrics like Reissner-Nordström, M2, M5

Calculated post-Newtonian parameters beta and gamma

Abstract

A family of spherically symmetric solutions in the model with 1-component anisotropic fluid is considered. The metric of the solution depends on a parameter q > 0 relating radial pressure and the density and contains n -1 parameters corresponding to Ricci-flat ``internal space'' metrics. For q = 1 and certain equations of state the metric coincides with the metric of black brane solutions in the model with antisymmetric form. A family of black hole solutions corresponding to natural numbers q = 1,2, ... is singled out. Certain examples of solutions (e.g. containing for q =1 Reissner-Nordstr\"{o}m, M2 and M5 black brane metrics) are considered. The post-Newtonian parameters beta and gamma corresponding to the 4-dimensional section of the metric are calculated.