Thermodynamics of Accelerating Black Holes

Abstract

We address a long-standing problem of describing the thermodynamics of an accelerating black hole. We derive a standard first law of black hole thermo- dynamics, with the usual identification of entropy proportional to the area of the event horizon — even though the event horizon contains a conical singularity. We show how to generalise this result, formulating thermodynamics for black holes with varying conical deficits. We derive a new potential for the varying tension defects: the thermodynamic length, both for accelerating and static black holes. We discuss possible physical processes in which the tension of a string ending on a black hole might vary, and also map out the thermodynamic phase space of accelerating black holes and explore their critical phenomena. We then revisit the critical limit in which asymptotically-AdS black holes develop maximal conical deficits, first for a stationary rotating black hole, and then for an accelerated black hole, by taking various upper bounds for the parameters in the spacetimes presented. We explore the thermodynamics of these geometries and evaluate the reverse isoperimetric inequal- ity, and argue that the ultra-spinning black hole only violates this condition when it is nonaccelerating. Finally, we return to some of our earlier findings and adjust them in light of new results; a new expression for the mass is obtained by computing the dual stress-energy tensor for the spacetime and finding that it corresponds to a relativistic fluid with a nontrivial viscous shear tensor. We compare the holographic computation with the method of conformal completion showing it yields the same result for the mass.