Complementary role of the pressure in the black hole thermodynamics

TL;DR

This paper explores how pressure terms in black hole thermodynamics influence entropy and energy, showing that decomposing pressure can reconcile thermodynamic energy with black hole mass and derive the Wald entropy.

Contribution

It demonstrates that decomposing pressure in black hole thermodynamics allows the thermodynamic energy to match the black hole mass and yields the Wald entropy.

Findings

Pressure decomposition aligns thermodynamic energy with black hole mass.

Corrected entropy follows the Wald entropy formula.

Pressure terms are crucial in black hole thermodynamic laws.

Abstract

In black hole thermodynamics of certain models, the thermodynamic first law may contain the pressure term. The corresponding entropy follows the area law whereas the thermodynamic energy is not the same with the black hole mass. If the pressure can be decomposed into two parts and recombined with the original thermodynamic quantities, then the thermodynamic energy becomes the black hole mass and the entropy satisfying the area law turns out to be the corrected entropy called the Wald entropy, respectively.