Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics

TL;DR

This paper calculates the Euclidean action for constant curvature black holes in Einstein AdS gravity, revealing their thermodynamic properties and showing they do not follow standard thermodynamic relations.

Contribution

It provides the first computation of the Euclidean action for CCBHs and analyzes their thermodynamic behavior within Einstein AdS gravity.

Findings

CCBH solutions have constant Riemann tensor and contain a de-Sitter brane.

The free energy computed does not satisfy standard thermodynamic relations.

These solutions extend the understanding of gravitational configurations in AdS space.

Abstract

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.