C-metric solution for conformal gravity with a conformally coupled scalar field

TL;DR

This paper presents a new C-metric solution in conformal gravity with a conformally coupled scalar field, exploring its geometric properties, horizons, and effects of conformal gauge choices.

Contribution

It introduces a novel C-metric solution in conformal gravity coupled with a scalar field, analyzing its physical regions and conformal invariance effects.

Findings

Solution is Petrov type D and conformal to AdS C-metric.

Identifies static regions and horizon structures.

Discusses influence of conformal gauge choices on spacetime.

Abstract

The C-metric solution of conformal gravity with a conformally coupled scalar field is presented. The solution belongs to the class of Petrov type D spacetimes and is conformal to the standard AdS C-metric appeared in vacuum Einstein gravity. For all parameter ranges, we identify some of the physically interesting static regions and the corresponding coordinate ranges. The solution may contain a black hole event horizon, an acceleration horizon, either of which may be cut by the conformal infinity or be hidden behind the conformal infinity. Since the model is conformally invariant, we also discussed the possible effects of the conformal gauge choices on the structure of the spacetime.