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.
Highlights
This establishment of geometrothermodynamics, as well as that introduced in Ref. [36], is a formalism that is used to designate a flat twodimensional space of equilibrium states, which is endowed with a thermodynamic metric
A more generalized consideration of geometrothermodynamics is available in Ref. [37], where the thermodynamics of the charged BTZ black hole is investigated in the context of the Weinhold and Ruppeiner geometries
In this paper we studied the thermodynamics of the BTZ black hole, based on the axiomatic approach of Carathéodory
Summary
The (2+1)-dimensional, uncharged, black hole solution with a negative cosmological constant Λ = − −2 is obtained from the action. Where B is a surface term [3,4]. For the stationary circular symmetry, the corresponding spacetime metric is given in terms of the coordinates −∞ < t < ∞, 0 < r < ∞, and 0 ≤ φ ≤ 2π , and can be written as ds2 = −N 2(r )c2dt2 + N −2(r )dr 2 +r 2 N φ(r )c dt + dφ 2 , (2). Page 3 of 9 499 in which the square lapse function and the angular shift are given, respectively, by
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