Pair of accelerated black holes in a de Sitter background: the dS C-metric

TL;DR

This paper analyzes the de Sitter C-metric describing a pair of accelerated black holes, providing detailed diagrams, embedding in higher-dimensional spacetime, and exploring physical properties and parameter ranges.

Contribution

It extends previous work by drawing Carter-Penrose diagrams, analyzing the embedding in 5D Minkowski space, and characterizing the physical properties and parameter ranges of the dS C-metric.

Findings

Carter-Penrose diagrams identify two non-interacting black holes.

Embedding in 5D Minkowski space visualizes black hole motion.

Parameter ranges for non-extreme, extreme black holes, and naked particles.

Abstract

Following the work of Kinnersley and Walker for flat spacetimes, we have analyzed the anti-de Sitter C-metric in a previous paper. In the de Sitter case, Podolsky and Griffiths have established that the de Sitter C-metric (dS C-metric) found by Plebanski and Demianski describes a pair of accelerated black holes in the dS background with the acceleration being provided (in addition to the cosmological constant) by a strut that pushes away the two black holes or, alternatively, by a string that pulls them. We extend their analysis mainly in four directions. First, we draw the Carter-Penrose diagrams of the massless uncharged dS C-metric, of the massive uncharged dS C-metric and of the massive charged dS C-metric. These diagrams allow us to clearly identify the presence of two dS black holes and to conclude that they cannot interact gravitationally. Second, we revisit the embedding of the dS C-metric in the 5D Minkowski spacetime and we represent the motion of the dS C-metric origin in the dS 4-hyperboloid as well as the localization of the strut. Third, we comment on the physical properties of the strut that connects the two black holes. Finally, we find the range of parameters that correspond to non-extreme black holes, extreme black holes, and naked particles.