Phase transition and entropy spectrum of BTZ black hole in three-dimensional gravity with torsion

Abstract

In this paper, we study the phase transition and the entropy spectrum of BTZ black hole obtained in a model of three-dimensional gravity with torsion. By calculating the heat capacity we find that the BTZ black hole we considered will experience phase transition at some critical point. This indicates that the critical behaviors of black holes do not only depend on the spacetime metric, but have to do with the theory of gravity under consideration. In addition we derived the entropy spectrum of the BTZ black hole according to the quasinormal modes(QNMs) and the adiabatic invariance. It shows that the area or entropy spectrum will also rely on the concrete gravitational action.

Quasi-local Energy in 3D Gravity with Torsion

“…in which we have introduced an effective AdS radius ℓ −2 eff ≡ −Λ eff . This is consistent with previous result in [28] via the Euclidean partition function approach 2 , as well as that in [29] via a direct integration from the first law. Our entropy formula (81) is also consistent with the generic expression for black hole entropy in Chern-Simons-like theories in Section XVI of [22] via a different approach employing the Lorentz-Lie derivative.…”

AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity

“…In Refs. [80][81][82][83][84] the authors discussed the positivity of the heat capacity and relate it to the local black hole thermodynamic stability condition. This means that the black holes will be thermodynamic stable if C V > 0.…”

Thermodynamic volume of cosmological solitons

“…From this perspective one can show that the celebrated Hawking-Page phase transition [19] can be understood as being analogous to a solid/liquid phase transition [1], and more generally that the 4-dimensional Reissner-Nordström AdS black hole can be interpreted as a Van der Waals fluid with the same critical exponents [13]. Along with more general Van der Waals behaviour with standard critical exponents [14,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], other 'chemical' black hole behaviour was subsequently discovered, such as reentrant phase transitions [37], tricritical points [38], Carnot cycles [39], isolated critical points [40,41], extensions to black rings [42], and superfluidity [43].…”