Thermodynamics of charged and accelerating black holes
Tomáš Hale, David Kubizňák, Jana Menšíková, Robert B. Mann, Jiayue Yang
Abstract
We reconsider various C-metric spacetimes describing charged and (slowly) accelerating AdS black holes in different theories of (nonlinear) electrodynamics and revisit their thermodynamic properties. Focusing first on the Maxwell theory, we find a parametrization of the metric where we can eliminate the nontrivial ``normalization'' of the boost Killing vector which was crucial for obtaining consistent thermodynamics in previous studies. We also calculate the Euclidean action using (i) the standard holographic renormalization and (ii) the topological renormalization, showing that in the presence of overall cosmic string tension the two do not agree. These results are also extended to accelerating black holes in ModMax and RegMax nonlinear electrodynamics. Interestingly, for the latter the electrostatic potential picks up a modification, that remains to be explained, but is consistent with the topological renormalization and the (generalized) Hawking-Ross prescription. Our study indicates that thermodynamics of charged accelerating black holes is far from being completely understood.