Accelerated black holes in an anti-de Sitter universe

TL;DR

This paper analyzes the global structure of the C-metric with a negative cosmological constant, revealing complex configurations of accelerated black holes in anti-de Sitter spacetime through conformal diagrams.

Contribution

It provides a detailed analysis of the spacetime structure of accelerated black holes in anti-de Sitter space, extending understanding beyond previous flat or de Sitter cases.

Findings

Spacetime can represent single or multiple accelerated black holes.

The structure varies with acceleration, showing different configurations.

Conformal diagrams illustrate the global spacetime structure.

Abstract

The C-metric is one of few known exact solutions of Einstein's field equations which describes the gravitational field of moving sources. For a vanishing or positive cosmological constant, the C-metric represents two accelerated black holes in asymptotically flat or de Sitter spacetime. For a negative cosmological constant the structure of the spacetime is more complicated. Depending on the value of the acceleration, it can represent one black hole or a sequence of pairs of accelerated black holes in the spacetime with an anti-de Sitter-like infinity. The global structure of this spacetime is analyzed and compared with an empty anti-de Sitter universe. It is illustrated by 3D conformal-like diagrams.