Neutral and charged matter in equilibrium with black holes

TL;DR

This paper investigates the conditions under which static equilibrium can exist between black holes and surrounding matter, exploring various matter types and revealing new equilibrium scenarios, especially involving charged black holes and vacuum fluids.

Contribution

It introduces new equilibrium conditions for black holes with different matter equations of state, extending known solutions like Majumdar-Papapetrou to more general cases.

Findings

Ultraextremal black holes cannot be in equilibrium without vacuum fluid.

Matter with positive w can surround extremal charged black holes if properly charged.

New equilibrium configurations generalizing Majumdar-Papapetrou conditions are identified.

Abstract

We study the conditions of a possible static equilibrium between spherically symmetric, electrically charged or neutral black holes and ambient matter. The following kinds of matter are considered: (1) neutral and charged matter with a linear equation of state p_r = w\rho (for neutral matter the results of our previous work are reproduced), (2) neutral and charged matter with p_r \sim \rho^m, m > 1, and (3) the possible presence of a "vacuum fluid" (the cosmological constant or, more generally, anything that satisfies the equality T^0_0 = T^1_1 at least at the horizon). We find a number of new cases of such an equilibrium, including those generalizing the well-known Majumdar-Papapetrou conditions for charged dust. It turns out, in particular, that ultraextremal black holes cannot be in equilibrium with any matter in the absence of a vacuum fluid; meanwhile, matter with w > 0, if it is properly charged, can surround an extremal charged black hole.