Thermodynamic instabilities of generalized exotic BTZ black holes

Abstract

We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume CV [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelbiom and Zanelli (BTZ) black holes and find that CV can be positive even when the reverse isoperimetric inequality is violated, providing a counter example to the conjecture. However in all cases where CV is positive, the specific heat at constant pressure CP is negative, indicating that generalized exotic black holes are thermodynamically unstable, suggesting that a broader version of the conjecture might hold.

Are “Superentropic” black holes superentropic?

“…It remains to be shown whether similar doubts could arise also for other Superentropic black holes, for example the recently studied charged BTZ black holes [57][58][59][60] have an apparently similar issue. The charged BTZ black hole is a three dimensional electrically charged solution of the Einstein-Maxwell equations [61]…”

“…We therefore suspect that the traditional thermodynamics of this somewhat pathological solution is most likely not the correct one. Finally, in an interesting recent twist, the rotating (uncharged) BTZ black hole, which as a traditional Einstein solution is not superentropic, can be reimagined as a solution of the gravitational Chern-Simons action [58,64]. The thermodynamic parameters become "exotic" (with mass and angular momentum charges reversed and the entropy no longer given by the horizon area).…”

“…This fascinating result has caused some puzzlement, as the thermodynamic parameters (4.6) are not obtained as an "a → " limit of the conventional parameters, (2.20), nor does it seem possible to obtain one of these black holes by some sort of continuous process. In addition, the idea that the entropy can be unbounded for a fixed volume suggests that superentropic black holes should be somehow unstable, a notion explored (in a different context) by Johnson [57], see also [58,59]. Thus the Superentropic black hole is worthy of further study.…”

Thermodynamic Instability of $\mathrm{3D}$ Einstein-Born-Infeld AdS Black Holes

“…This result consequently leads to a natural conjecture that super-entropic black holes always have C V < 0, making them unstable in the extended thermodynamics. Later, it was found that this conjecture is violated for generalized exotic BTZ black holes in some parameter region [24]. However in this case, the specific heat at constant pressure C P was exhibited to be negative whenever C V > 0.…”

“…More relevant discussions can be found in refs. [16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”