Adiabatic evolution of Hayward black hole

TL;DR

This paper applies Carathéodory's thermodynamics to the Hayward black hole, analyzing adiabatic paths, extremal boundaries, and black hole mergers to understand their thermodynamic behavior and law preservation.

Contribution

It introduces a thermodynamic manifold for the Hayward black hole using Carathéodory's approach, highlighting the extremal boundary as an adiabatic disconnect and analyzing black hole mergers.

Findings

Adiabatic paths are confined to the non-extremal manifold.

The second and third laws are preserved in the thermodynamic analysis.

Extremal black holes form an adiabatically disconnected boundary.

Abstract

In this letter we use the Carath\'{e}odory's approach to thermodynamics, to construct the thermodynamic manifold of the Hayward black hole. The Pfaffian form representing the infinitesimal heat exchange reversibly is considered to be $\delta Q_{\mathrm{rev}}\equiv {\rm d}r_s-\mathcal{F}_H {\rm d}l$, previously obtained by Molina \& Villanueva \cite{fmv20}, where $r_s$ is the Schwarzschild radius, $l$ is the Hayward's parameter responsible for the possible regularization of the Schwarzschild black hole, and $\mathcal{F}_H$ is the intensive variable called the Hayward's force. By solving the associated Cauchy problem, the adiabatic paths are confined to the non-extremal manifold, and therefore, the status of the second and third laws are preserved. Consequently, the extremal sub-manifold corresponds to the {adiabatically disconnected} boundary of the manifold. In addition, the merger of two extremal Hayward black holes is analyzed.