Accelerating Black Holes

Ruth Gregory

doi:10.1088/1742-6596/942/1/012002

Abstract

In this presentation, I review recent work [1, 2] with Mike Appels and David Kubizňák on thermodynamics of accelerating black holes. I start by reviewing the geometry of accelerating black holes, focussing on the conical deficit responsible for the ‘force’ causing the black hole to accelerate. Then I discuss black hole thermodynamics with conical deficits, showing how to include the tension of the deficit as a thermodynamic variable, and introducing a canonically conjugate thermodynamic length. Finally, I describe the thermodynamics of the slowly accelerating black hole in anti-de Sitter spacetime.

Highlights

Black holes have proved to be perennially fascinating objects to study, both from the theoretical and practical points of view
The geometry looks like a black hole in AdS displaced from the centre, the force required to hold it being supplied by the cosmic string or conical deficit running from the horizon to the boundary
Because the energy of the black hole has been fixed, the event horizon moves outwards to compensate for the conical deficit, resulting in an increase of entropy indicating this is an irreversible thermodynamic process

Summary

Introduction

Black holes have proved to be perennially fascinating objects to study, both from the theoretical and practical points of view. The geometry looks like a black hole in AdS displaced from the centre, the force required to hold it being supplied by the cosmic string or conical deficit running from the horizon to the boundary. Interpreting this tension as the force, and A as the acceleration, Newton’s Law suggests that the mass of the black hole should be identified as M = m/K, so that μ = F = M A – we will see presently that this is exactly what the first law of thermodynamics requires

Thermodynamics with conical defects

Exploring thermodynamics

Conclusion