Adiabatic analysis of the rotating BTZ black hole

TL;DR

This paper investigates the thermodynamics of rotating BTZ black holes using an adiabatic approach based on Carathéodory's axiomatic framework, analyzing transformations and implications for black hole thermodynamic laws.

Contribution

It introduces an adiabatic analysis of rotating BTZ black holes using Pfaffian forms and explores the thermodynamic laws and extremal black hole merging.

Findings

Derived adiabatic transformations for BTZ black holes.

Discussed implications for the second and third laws of thermodynamics.

Analyzed the merging process of extremal black holes.

Abstract

In this paper we analyze some interesting features of the thermodynamics of the rotating BTZ black hole from the Carath\'{e}odory axiomatic postulate, for which, we exploit the appropriate Pfaffian form. The allowed adiabatic transformations are then obtained by solving the corresponding Cauchy problem, and are studied accordingly. Furthermore, we discuss the implications of our approach, regarding the the second and third laws of black hole thermodynamics. In particular, the merging of two extremal black holes is studied in detail.