Cosmological Multi-Black Hole Solutions

TL;DR

This paper introduces analytic solutions describing multiple charged black holes in a universe with positive cosmological constant, capturing their dynamics, interactions, and thermodynamics in de Sitter spacetime.

Contribution

It provides the first analytic models of coalescing black holes with a positive cosmological constant, extending known solutions to dynamic, multi-black-hole scenarios.

Findings

Solutions describe moving, merging black holes in de Sitter space.

Black holes with charge equal to mass are in thermal equilibrium with Hawking radiation individually.

Dynamic solutions lack a global equilibrium temperature but approximate states exist in certain limits.

Abstract

We present simple, analytic solutions to the Einstein-Maxwell equation, which describe an arbitrary number of charged black holes in a spacetime with positive cosmological constant $\Lambda$. In the limit $\Lambda=0$, these solutions reduce to the well known Majumdar-Papapetrou (MP) solutions. Like the MP solutions, each black hole in a $\Lambda >0$ solution has charge $Q$ equal to its mass $M$, up to a possible overall sign. Unlike the $\Lambda = 0$ limit, however, solutions with $\Lambda >0$ are highly dynamical. The black holes move with respect to one another, following natural trajectories in the background deSitter spacetime. Black holes moving apart eventually go out of causal contact. Black holes on approaching trajectories ultimately merge. To our knowledge, these solutions give the first analytic description of coalescing black holes. Likewise, the thermodynamics of the $\Lambda >0$ solutions is quite interesting. Taken individually, a $|Q|=M$ black hole is in thermal equilibrium with the background deSitter Hawking radiation. With more than one black hole, because the solutions are not static, no global equilibrium temperature can be defined. In appropriate limits, however, when the black holes are either close together or far apart, approximate equilibrium states are established.