Inverted equation of state and general approach to vacuum-like configurations

Abstract

We consider spherically symmetric static black hole configurations that obey the vacuum equation of state: $p_{r}=-ρ$, where $p_{r}$ is the radial pressure, $ρ$ being energy density. We find in a closed form the metric for an arbitrary equation of state for tangential pressure $p_{θ}(ρ)$. The corresponding formulas enable us to embrace compact Schwarzschild-like configurations and dispersed systems. They include metrics with a regular center and singular ones. In a particular case, the metric of the Kiselev black hole is reproduced.