Entropy of Constant Curvature Black Holes in General Relativity

TL;DR

This paper investigates the unique thermodynamic properties of constant curvature black holes in General Relativity, revealing unconventional entropy associations and thermodynamic behaviors due to their unusual topology.

Contribution

It demonstrates how to compute entropy and quasilocal thermodynamics for these black holes, highlighting their distinct properties compared to typical black hole spacetimes.

Findings

Entropy is associated with the region between the event horizon and the observer.

Surfaces of constant internal energy are not isotherms.

The first law of thermodynamics holds only in an integral form.

Abstract

We consider the thermodynamic properties of the constant curvature black hole solution recently found by Banados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton.