Adiabatic analysis of the rotating BTZ black hole
Mohsen Fathi (Instituto de Física y Astronomía, Universidad de Valparaíso, Avenida Gran Bretaña 1111, Valparaíso, Chile); Samuel Lepe (Instituto de Física, Pontificia Universidad de Católica de Valparaíso, Avenida Brasil 2950, Valparaíso, Chile); J. Villanueva (Instituto de Física y Astronomía, Universidad de Valparaíso, Avenida Gran Bretaña 1111, Valparaíso, Chile)
In this paper we analyze some interesting features of the thermodynamics of the rotating BTZ black hole from the Carathéodory 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 second and third laws of black hole thermodynamics. In particular, the merging of two extremal black holes is studied in detail.