A new form of the rotating C-metric

TL;DR

This paper introduces a new, simpler form of the rotating charged C-metric that avoids problematic singularities, making the analysis of accelerating rotating black holes more straightforward and physically consistent.

Contribution

It proposes an analogous new form for the rotating charged C-metric with a factorizable structure function, distinct from the traditional form, and clarifies its physical advantages.

Findings

The new form simplifies the analysis of the rotating C-metric.

It eliminates torsion singularities and closed timelike curves.

The new form is a natural generalization of the non-rotating case.

Abstract

In a previous paper, we showed that the traditional form of the charged C-metric can be transformed, by a change of coordinates, into one with an explicitly factorizable structure function. This new form of the C-metric has the advantage that its properties become much simpler to analyze. In this paper, we propose an analogous new form for the rotating charged C-metric, with structure function G(\xi)=(1-\xi^2)(1+r_{+}A\xi)(1+r_{-}A\xi), where r_\pm are the usual locations of the horizons in the Kerr-Newman black hole. Unlike the non-rotating case, this new form is not related to the traditional one by a coordinate transformation. We show that the physical distinction between these two forms of the rotating C-metric lies in the nature of the conical singularities causing the black holes to accelerate apart: the new form is free of torsion singularities and therefore does not contain any closed timelike curves. We claim that this new form should be considered the natural generalization of the C-metric with rotation.