Charged C-metric with conformally coupled scalar field

TL;DR

This paper generalizes the charged C-metric to include a conformally coupled scalar field with a cosmological constant, revealing conditions under which the scalar field remains regular and the spacetime describes an accelerating black string.

Contribution

It introduces a new solution combining charge, scalar field, and cosmological constant, showing how the scalar field's singularities can be avoided in certain regimes.

Findings

Scalar field blows up only at the pole without cosmological constant

Cosmological constant can regularize the scalar field across the horizon

For negative cosmological constant, the solution describes a regular black string

Abstract

We present a generalisation of the charged C-metric conformally coupled with a scalar field in the presence of a cosmological constant. The solution is asymptotically flat or a constant curvature spacetime. The spacetime metric has the geometry of a usual charged C-metric with cosmological constant, where the mass and charge are equal. When the cosmological constant is absent it is found that the scalar field only blows up at the angular pole of the event horizon. The presence of the cosmological constant can generically render the scalar field regular where the metric is regular, pushing the singularity beyond the event horizon. For certain cases of enhanced acceleration with a negative cosmological constant, the conical singularity disappears all together and the scalar field is everywhere regular. The black hole is then rather a black string with its event horizon extending all the way to asymptotic infinity and providing itself the necessary acceleration.