A new form of the C-metric with cosmological constant

TL;DR

This paper extends a known form of the C-metric to include a cosmological constant, providing a new parameterization and visualization of the solution's domain structure, including potential shapes like triangles and trapezoids.

Contribution

It introduces a partially factorized form of the C-metric with a cosmological constant and a novel domain structure representation based on the roots of structure functions.

Findings

The solution is fully parameterized by the edges of a 'box' in the domain structure.

The roots of the structure functions serve as fundamental parameters.

Possible domain shapes include box, triangle, and trapezoid configurations.

Abstract

The new form of the C-metric proposed by Hong and Teo, in which the two structure functions are factorised, has proved useful in its analysis. In this paper, we extend this form to the case when a cosmological constant is present. The new form of this solution has two structure functions which are partially factorised; moreover, the roots of the structure functions are now regarded as fundamental parameters. This leads to a natural representation of the solution in terms of its so-called domain structure, in which the allowed coordinate range can be visualised as a "box" in a two-dimensional plot. The solution is then completely parameterised by the locations of the edges of this box, at least in the uncharged case. We also briefly analyse other possible domain structures---in the shape of a triangle and trapezoid---that might describe physically interesting space-times within the AdS C-metric.