Conformally invariant thermodynamics of a Maxwell-Dilaton black hole

TL;DR

This paper investigates the thermodynamics of Maxwell-Dilaton black holes, analyzing different surface gravity definitions, and proposes a frame-independent entropy consistent with the third law of black hole mechanics.

Contribution

It provides a frame-independent entropy and temperature for Maxwell-Dilaton black holes, addressing extremal configurations and singularity structures using holographic arguments.

Findings

Different surface gravity definitions yield varying predictions near extremality.

A holographic approach removes micro-states from disconnected regions.

The proposed entropy and temperature align with standard results and the third law.

Abstract

The thermodynamics of Maxwell-Dilaton (dirty) black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We explore a set of definitions for the surface gravity and observe the different predictions they make for the near extremal configuration of this black hole. Finally, motivated by the singularity structure in the interior of the event horizon, we use a holographic argument to remove the micro-states from the disconnected region of this solution. In this manner, we construct a frame independent entropy from which we obtain a temperature which agrees with the standard results in the non-extremal regime, and has a desirable behaviour around the extremal configurations according to the third law of black hole mechanics.