Simpson-Visser-AdS Black Holes: Thermodynamics and Binary Merger

TL;DR

This work extends Simpson-Visser regularization to AdS black holes to produce SV-AdS geometries that are free of central singularities. It develops a thermodynamic framework with the first-law form $dM=TdS$ and derives an $a$-dependent entropy, recovering the standard $S=\pi r_h^2$ as $a\to0$, while revealing an extremal limit and no Hawking–Page transition. The study uncovers a rich phase structure: SV-AdS black holes exhibit a van der Waals–like small/large black hole transition with a critical point controlled by $a$, and the standard thermal AdS phase is replaced by a black-hole-dominated regime for all temperatures. Additionally, the authors analyze mergers of equal-mass SV-AdS and SV-flat black holes under the second law, finding a nonmonotonic dependence of the final mass on $a$ and discussing potential observational bounds from gravitational-wave data. These results demonstrate how SV regularization fundamentally alters black hole thermodynamics and merger energetics, offering a pathway to constrain the regularization parameter and explore critical dynamics in gravitational systems.

Abstract

In this article, we performed Simpson-Visser (SV)-regularization scheme to Anti-de Sitter (AdS) black holes and then studied thermal properties of the resulting spacetime geometry. We considered the validity of the first law of black hole thermodynamics in this case and derived an entropy formula consistent with this new regular geometry. Next, we carried out the free energy analysis and studied the phase structure of these black holes. We discovered non-trivial phase transition properties dependent on the SV-regularization parameter. We also considered the validity of the second law of black hole thermodynamics and analyzed a merger scenario of two equal mass SV-regular black holes. In particular, we investigated the impact of the SV-regularization parameter on the constraints on post-merger black hole mass. Intrestingly, we found that the bounds initially increase and then fall sharply with increasing the SV-regularization parameter. All results are compared with standard black holes for vanishing SV-regularization parameter.

Figures (6)

• Figure 1: Hawking temperature vs horizon radius for SV-regular AdS black holes for $a=(0, 0.1, 0.2, 0.3)$ as we set $l=1$.
• Figure 2: Free energy vs Hawking temperature for SV-AdS regular black holes for $a=(0, 0.1, 0.2, 0.3)$ as we set $l=1$.
• Figure 3: Final Mass vs SV-Regularization Parameter $a$ as we set $l=1$ and $M_i=1$.
• Figure 4: Final Mass vs SV-Regularization Parameter $a$ as we set $l=1$ and $M_i=1,2,3$.
• Figure 5: Final Mass vs SV-Regularization Parameter $a$ as we set $l=\infty$, $M_i=1$.