Static black holes in equilibrium with matter: nonlinear equation of state

TL;DR

This paper investigates conditions under which a spherically symmetric black hole can be in equilibrium with surrounding matter characterized by a nonlinear radial pressure-density relationship, revealing restrictions for perfect fluids and anisotropic cases.

Contribution

It generalizes previous linear equation of state results to nonlinear cases and explores equilibrium conditions for anisotropic matter near black hole horizons.

Findings

Perfect fluid near horizon requires approximately linear equation of state.

In anisotropic cases, no restriction on equation of state but horizon must be simple.

Derived conditions for equilibrium depend on pressure anisotropy and equation of state.

Abstract

We consider a spherically symmetric black hole in equilibrium with surrounding classical matter that is characterized by a nonlinear dependence of the radial pressure p_{r} on the density {\rho}. We examine under which requirements such an equilibrium is possible. It is shown that if the radial and transverse pressures are equal (Pascal perfect fluid), equation of state should be approximately linear near the horizon. The corresponding restriction on ((dp_{r})/(d{\rho})) is a direct generalization of the result, previously found for an exactly linear equation of state. In the anisotropic case there is no restriction on equation of state but the horizon should be simple (nondegenerate).