Thermal Action and Specific Heat of the Five-Dimensional Non-Extremal Black Hole

TL;DR

This paper constructs the Euclidean action for a five-dimensional non-extremal black hole with multiple charges, linking it to entropy and revealing a phase transition through specific heat analysis.

Contribution

It introduces a method to compute the thermal action for complex black holes and relates it to their entropy and phase behavior, expanding understanding of higher-dimensional black hole thermodynamics.

Findings

Thermal action equals half the black hole entropy.

A phase transition is observed via specific heat calculations.

The results relate to the generalized Smarr formula.

Abstract

We construct the Euclidean on-shell action for the five-dimensional non-extremal black hole with multiple electric charges. We show that this thermal action agrees with one half of the entropy. This agreement is argued to be related to the generalized Smarr formula of the five-dimensional black hole mass. Through the calculation of the specific heat far off extremality we observe that a phase transition occurs.