Thermodynamically massless Simpson-Visser black holes

Abstract

In this work, we scrutinize the thermodynamic properties of the Simpson-Visser (SV) spacetime. Working within Einstein gravity coupled to nonlinear electrodynamics (NLED) and a scalar field with negative kinetic energy, we rederive the solution in a formulation where the integration constants do not explicitly appear in the action, allowing them to vary consistently in the thermodynamic analysis. Using the Euclidean method, we show that the regular spacetime structure modifies the boundary contributions to the conserved charge associated with time translations, allowing the NLED sector to cancel the mass term and yielding a black hole with vanishing thermodynamic mass. Nevertheless, the spacetime admits a conserved magnetic charge and describes a regular black hole with a single horizon, finite temperature, and entropy, while the first law of thermodynamics holds in a modified form. We further compare this solution with the corresponding scalar-free singular black hole obtained when the regular parameter vanishes. Placing the two configurations in the same heat bath with identical temperature and magnetic chemical potential, we find that the SV regular black hole always has a larger free energy, indicating that the scalar-free singular configuration is thermodynamically preferred.

Figures (3)

• Figure 1: Metric function $F(r)$ versus the dimensionless radius $r/\alpha$ for different values of $\alpha^2|h_1|$. The dots mark the wormhole throat radius. For sufficiently large $\alpha^2|h_1|$ the spacetime admits configurations where the event horizon lies outside the throat, describing regular black-hole geometries.
• Figure 2: Temperature $T_0(\rho_h)$ of the scalar-free black-hole solution as a function of the horizon radius $\rho_h$ for several values of the dimensionless parameter $q/f_1^{\,2}$. The dots mark the extrema of the temperature, which separate the small and large black-hole branches and signal the onset of thermodynamic phase transitions.
• Figure 3: Free energy of the two configurations as a function of the core scale $\alpha$ for several values of $h_1$. The upper-left panel shows the free energy $\mathcal{G}(\alpha)$ of the reconstructed Simpson-Visser regular black hole, while the upper-right panel shows the free energy $\mathcal{G}_0(\alpha)$ of the corresponding scalar-free black hole in the same heat bath with identical temperature and magnetic chemical potential. The lower panel displays their difference $\mathcal{G}(\alpha)-\mathcal{G}_0(\alpha)$, which is always positive, indicating that the scalar-free configuration is thermodynamically preferred.