Interpreting the C-metric

TL;DR

This paper provides a clearer understanding of the C-metric by employing new coordinate systems to explicitly analyze the global causal structure and interpret its parameters.

Contribution

It introduces simplified coordinate systems for the C-metric, enabling explicit extensions and a comprehensive causal diagram, enhancing understanding of black hole acceleration.

Findings

Explicit Kruskal-Szekeres extensions obtained

Conformal Penrose diagrams constructed

Physical interpretation of metric parameters provided

Abstract

The basic properties of the C-metric are well known. It describes a pair of causally separated black holes which accelerate in opposite directions under the action of forces represented by conical singularities. However, these properties can be demonstrated much more transparently by making use of recently developed coordinate systems for which the metric functions have a simple factor structure. These enable us to obtain explicit Kruskal-Szekeres-type extensions through the horizons and construct two-dimensional conformal Penrose diagrams. We then combine these into a three-dimensional picture which illustrates the global causal structure of the space-time outside the black hole horizons. Using both the weak field limit and some invariant quantities, we give a direct physical interpretation of the parameters which appear in the new form of the metric. For completeness, relations to other familiar coordinate systems are also discussed.