Black Hole Entropy Bounded by the Specific Heat

TL;DR

This paper establishes new bounds on black hole entropy based on the specific heat at fixed charges, extending thermodynamic inequalities to include derivatives for various black hole types.

Contribution

It introduces novel bounds on black hole entropy related to specific heat, applicable to both static and rotating black holes, extending previous thermodynamic inequalities.

Findings

Bounds proven for spherically-symmetric static black holes

Bounds tested on diverse static and rotating black holes

Extension of algebraic inequalities to derivatives of thermodynamic variables

Abstract

We propose new bounds on black hole entropy in terms of the specific heat at fixed charges. For special spherically-symmetric and static black holes ($g_{tt} g_{rr}=-1$), we prove the bounds with suitable sufficient energy conditions. For more general static and rotating black holes, we test the bounds with a variety of examples. This work extends the previously-known algebraic inequalities of the black hole thermodynamic variables such as the Penrose inequality, to include their derivatives.