Black Holes with Topological Defects: The C-metric in Three and Four Dimensions

Abstract

We examine the effects of accelerating both isolated and coupled black
holes in a variety of contexts.

A detailed investigation of the thermodynamic phase space of a charged, rotating,
and accelerating black hole placed in a background of negative cosmological constant
is performed, and novel effects due to acceleration are identified. A modified
Christodoulou-Ruffini formula for the solution is shown to hold, providing compelling
evidence that the mass used, identified using holographic techniques, is the correct
one.

Motivated by the holographic results, we then identify the mass of an array of black
holes connected by conical deficits and without cosmological constant, of which the
C-metric is a special case. This mass is shown to obey a first law of thermodynamics,
with the string tensions acting as a thermodynamic charge. The black holes are
coupled in such a way that a variation applied to one affects all of the others. A
similar Christodoulou-Ruffini formula is shown to hold in this context.

We then examine a family of three-dimensional solutions analogous to the four-dimensional C-metric.
We identify three classes of geometry. From these, we construct stationary,
accelerating conical deficits; novel one-parameter extensions of
the static BTZ family which resemble the C-metric; and braneworld solutions. We
comment on the extent to which our solutions may be considered "accelerating black
holes".