On black hole solutions in model with anisotropic fluid

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-Nordström, 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.