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

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"

Conical holographic heat engines

We demonstrate that adding a conical deficit to a black hole holographic heat engine increases its efficiency; in contrast, allowing a black hole to accelerate decreases efficiency if the same average conical deficit is maintained. Adding other charges to the black hole does not change this qualitative effect. We also present a simple formula to calculate the efficiency of elliptical cycles for any black hole, which allows a more efficient numerical algorithm for computation

Accelerating black hole chemistry

We introduce a new set of chemical variables for the accelerating black hole. We show how these expressions suggest that conical defects emerging from a black hole can be considered as true hair – a new charge that the black hole can carry – and discuss the impact of conical deficits on black hole thermodynamics from this ‘chemical’ perspective. We conclude by proving a new Reverse Isoperimetric Inequality for black holes with conical defects

On acceleration in three dimensions

We go “back to basics”, studying accelerating systems in 2 + 1 AdS gravity ab initio. We find three classes of geometry, which we interpret by studying holographically their physical parameters. From these, we construct stationary, accelerating point particles; one-parameter extensions of the BTZ family resembling an accelerating black hole; and find new solutions including a novel accelerating “BTZ geometry” not continuously connected to the BTZ black hole as well as some black funnel solutions

Thermodynamics of Many Black Holes

We discuss the thermodynamics of an array of collinear black holes which may be accelerating. We prove a general First Law, including variations in the tensions of strings linking and accelerating the black holes. We analyse the implications of the First Law in a number of instructive cases, including that of the C-metric, and relate our findings to the previously obtained thermodynamics of slowly accelerating black holes in anti-de Sitter spacetime. The concept of thermodynamic length is found to be robust and a Christoudoulou-Ruffini formula for the C-metric is shown