Thermodynamics of charged and accelerating black holes

TL;DR

This paper investigates the thermodynamics of charged, accelerating AdS black holes across different electrodynamics theories, clarifying previous inconsistencies and extending results to non-linear models.

Contribution

It introduces a new parametrization eliminating normalization issues and compares holographic and topological renormalization methods for these black holes.

Findings

Consistent thermodynamics achieved with new parametrization.

Discrepancies found between holographic and topological renormalization in certain cases.

Electrostatic potential modified in non-linear electrodynamics, aligning with generalized prescriptions.

Abstract

We reconsider various C-metric spacetimes describing charged and (slowly) accelerating AdS black holes in different theories of (non-linear) electrodynamics and revisit their thermodynamic properties. Focusing first on the Maxwell theory, we find a parametrization of the metric where we can eliminate the non-trivial `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) using 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 non-linear 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.