Adiabatic analysis of the rotating BTZ black hole

Abstract

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.

Carathéodory’s thermodynamics of the Schwarzschild black hole surrounded by quintessence

“…Together with the approach given by Gibbs [24], the Carathéodory's method and its further developments by Born [25], form the foundations of the so-called Geometrothermodynamics [26]. The link between the methods of Carathéodory and Gibbs, is however, argued to be established in terms of the homogeneity of the Pfaffian form δQ rev , as the infinitesimal heat exchange reversibly [27], and this method has been applied to the laws of black hole thermodynamics in [28][29][30][31][32], and recently, in [33][34][35] regarding the adiabatic (isoareal) processes of Hayward and BTZ BHs. The geometric formulation of the Carathéodory's method, makes it possible to have a self-contained study of the black hole thermodynamics, by using only the respected spacetime structure.…”