Regular black holes in isothermal cavity

TL;DR

The paper tackles the thermodynamics of regular (non-singular) black holes placed inside a finite isothermal cavity, formulating a reduced Euclidean action for a general regular BH metric in a canonical ensemble. It introduces a fluid-like anisotropic source to model the regular core and shows that short-distance quantum corrections enter the action, while at large distances the action recovers the classical singular BH-in-a-cavity form. Specializing to the noncommutative Schwarzschild black hole, the authors demonstrate a small/large stable black hole phase transition within the cavity, analogous to a Van der Waals liquid/gas transition, and show that the existence of this transition depends on the cavity radius, $r_c$, relative to a critical scale $r_i$. The results indicate that confinement via a cavity plays a role similar to AdS spacetime in stabilizing black holes and shaping their phase structure, providing a consistent thermodynamic framework for UV-regular spacetimes.

Abstract

We examine the thermodynamic behavior of a static neutral regular (non-singular) black hole enclosed in a finite isothermal cavity. The cavity enclosure helps us investigate black hole systems in a canonical or a grand canonical ensemble. Here we demonstrate the derivation of the reduced action for the general metric of a regular black hole in a cavity by considering a canonical ensemble. The new expression of the action contains quantum corrections at short distances and concludes to the action of a singular black hole in a cavity at large distances. We apply this formalism to the noncommutative Schwarzschild black hole, in order to study the phase structure of the system. We conclude to a possible small/large stable regular black hole transition inside the cavity that exists neither at the system of a classical Schwarzschild black hole in a cavity, nor at the asymptotically flat regular black hole without the cavity. This phase transition seems to be similar with the liquid/gas transition of a Van der Waals gas.

Figures (4)

• Figure 1: The red solid curve represents the noncommutative black hole temperature $T$vs$r_+$ in $\sqrt{\theta}$ units, while the dashed black curve represents the Hawking temperature of a classical Schwarzschild black hole, appearing an ultraviolet divergence to the final stage of the evaporation.
• Figure 2: The noncommutative black hole temperature $T$ inside the cavity vs$r_+$ in $\sqrt{\theta}$ units, for $r_{\mathrm{c}}=17 \sqrt{\theta}$ (red solid curve), for $r_{\mathrm{c}} = r_{\mathrm{i}} \simeq 10.913 \sqrt{\theta}$ (black dashed curve) and for $r_{\mathrm{c}}=9 \sqrt{\theta}$ (blue solid curve).
• Figure 3: The heat capacity $C$ of the noncommutative black hole inside the cavity vs$r_+$ in $\sqrt{\theta}$ units, for $r_{\mathrm{c}}=17 \sqrt{\theta}$ (red solid curve), for $r_{\mathrm{c}} = r_{\mathrm{i}} \simeq 10.913 \sqrt{\theta}$ (black dashed curve) and for $r_{\mathrm{c}}=9 \sqrt{\theta}$ (blue solid curve).
• Figure 4: The free energy $F$ of the noncommutative black hole inside the cavity vs$r_+$ in $\sqrt{\theta}$ units, for $r_{\mathrm{c}}=17 \sqrt{\theta}$ (red solid curve), for $r_{\mathrm{c}} = r_{\mathrm{i}} \simeq 10.913 \sqrt{\theta}$ (black dashed curve) and for $r_{\mathrm{c}}=9 \sqrt{\theta}$ (blue solid curve).