Thermodynamics of Reissner-nordstorm black bounce black hole

TL;DR

This paper investigates the thermodynamics of a charged, regular black hole model—the Reissner–Nordström black-bounce black hole—by extending the Simpson–Visser black-bounce spacetime to include Maxwell electromagnetism via an anisotropic fluid. The authors derive the thermodynamic quantities $M(S)$, $T(S)$, $C(S)$, $F(S)$, and $G(S)$ and analyze them in an extended phase space with pressure $P=\frac{3}{8\pi l^2}$ and volume $V=\frac{4}{3}\pi r^3$, showing a consistent single-phase behavior in $P$–$V$ isotherms. They further incorporate logarithmic entropy corrections from thermal fluctuations and CFT, obtaining $S_{THC}$ and $S_{CFT}$ and showing the quantum corrections dominate for small horizon radii while thermal corrections dominate for larger radii. The results indicate a phase-transition signal in the entropy and thermodynamic curves but no clear first-order Hawking–Page-type transition within the studied parameter range, highlighting a scale-dependent interplay between quantum and thermal effects in regular black holes.

Abstract

Black bounce black holes are the black holes which extend classical black hole solution to regularize singularity using a bouncing parameter. In our work, we explore the thermodynamics of Reissnernordstorm black-bounce black hole, mainly focused on the thermodynamic parameters such as entropy, mass, temperature, heat capacity and free energies(Helmholtz free energy and Gibbs Free energy). Along with that we investigated the inter relation between entropy and other thermodynamic parameters by plotting graphs. Additionally, studied the extended phase space which showed a possible phase transition in the above mentioned black hole and also determined the logarithmic correction to entropy term.

Figures (11)

• Figure 1: The figure shows the variation of $f(r)$ with the horizon radius $r$, where $Q = 0.1$. The red line illustrates the variation when $l = 0$, the blue line illustrates the variation when $l = 1$, and the green line illustrates the variation when $l = 1.5$.
• Figure 2: The figure shows the variation of Mass $M$ with Entropy $S$, where $Q = 0.1$. The red line illustrates the variation when $l = 0$, the blue line illustrates the variation when $l = 1$, and the green line illustrates the variation when $l = 1.5$. But all the three lines overlap completely,this indicates the variation of mass with entropy for every point is identical as a result only green line is visible.
• Figure 3: The figure shows the variation of Temperature $T$ with Entropy $S$, where $Q = 0.1$. The red line illustrates the variation when $l = 0$, the blue line illustrates the variation when $l = 1$, and the green line illustrates the variation when $l = 1.5$.But here the blue line overlaps with the green line indicating at $l = 1$ and $l = 1.5$ the variation of temperature with entropy is identical at these points.
• Figure 4: The figure shows the variation of Heat Capacity $C$ with the Entropy $S$, where $Q = 0.1$. The red line illustrates the variation when $l = 0$, the blue line illustrates the variation when $l = 1$, and the green line illustrates the variation when $l = 1.5$.
• Figure 5: The figure shows the variation of free energy $F$ with the Entropy $S$, where $Q = 0.1$. The red line illustrates the variation when $l = 0$, the blue line illustrates the variation when $l = 1$, and the green line illustrates the variation when $l = 1.5$, again here the blue line overlaps with the green line indicating at $l = 1$ and $l = 1.5$ the variation of free energy with entropy is identical at these points