Charged Simpson-Visser AdS Black Holes: Geodesic Structure and Thermodynamic Properties

TL;DR

This work applies Simpson-Visser regularization to a charged AdS black hole, constructing a regular geometry described by f(r)=1-2M/√(r^2+a^2)+Q^2/(r^2+a^2)+(r^2+a^2)/ℓ_p^2 and h^2(r)=r^2+a^2, with A_t=-Q/h(r). It analyzes null geodesics, the photon sphere, and the black hole shadow, deriving weak-deflection corrections hat{alpha} in terms of M, Q, and a, and computes observationally relevant shadow radii that are compared to EHT data for M87* and Sgr A*, constraining Q and the SV parameter a. The paper also studies charged-particle dynamics, including circular orbits and orbit types, and develops the BV-like thermodynamics in extended phase space, yielding expressions for M, T, S, F, and C_P, all modified by the SV parameter a. Finally, it shows that the SV regularization reshapes the equation of state and phase structure, potentially eliminating the classic Hawking-Page transition and introducing a rich, a-dependent critical behavior that connects microscopic regularization to macroscopic observables, with current EHT data providing bounds on the charge while leaving a loosely constrained.

Abstract

In this article, we apply the Simpson-Visser (SV) regularization scheme to Anti-de Sitter (AdS) charged black holes and investigate the resulting spacetime geometry in detail, with emphasis on both geodesic structure and thermodynamic behavior. In particular, we analyze the motion of massless particle, focusing on key features such as the photon sphere, black hole shadow, photon trajectory and the dynamics of charged particles, including the characteristics of the circular and type of orbits. Furthermore, we compare the theoretical predictions of the charged SV-AdS black hole with recent observations reported by the Event Horizon telescope (EHT) for M87* and Sgr~A*. Beyond the geodesic analysis, we explore the thermodynamics of the regularized charged SV-AdS black hole by deriving essential quantities such as the Hawking temperature, Gibbs free energy, and specific heat capacity. Through a systematic examination of these thermodynamic variables, we demonstrate how the regularization parameter inherent in the SV regularization influences particle dynamics, stability conditions, and the overall thermal properties of the modified black hole solution. This comprehensive study highlights the interplay between regularization effects and the physical observables associated with charged AdS black holes.

Figures (15)

• Figure 1: The profiles of $V_\mathrm{eff}(r)$, plotted for $\ell_p=500 M$ and $L = 1 M$, versus (a) changes in $Q$ while $a = 0.1 M$, and (b) changes in $a$ while $Q=0.2 M$.
• Figure 2: A typical radial profile of the effective potential is shown together with the corresponding shape of equatorial null geodesic orbits plotted in the for specific values of the spacetime parameters $a$ and $Q$, assuming $L = 1 M$ and $\ell_p = 500 M$. The characteristic radii for this case are: $r_h = 1.977 M$, $r_d = 4.572 M$, $r_f = 2.318 M$, and $r_p = 2.971 M$. In the orbit diagram, the black disk represents the event-horizon radius $r = r_h$, while the dashed green circle denotes the photon-sphere radius $r = r_p$. Furthermore, the black, yellow, and red trajectories correspond to photons executing zero, one, and two half-orbits around the black hole, respectively, before being deflected away from or captured by the black hole.
• Figure 3: The $b$-profiles of the weak deflection angle, plotted for $\ell_p = 500 M$, for changes of (a) $Q$ while $a=0.1 M$, and (b) $a=0.1 M$ while $Q=0.2 M$. The black dashed curve in the diagrams, corresponds to the weak deflection angle in the Schwazschild-AdS spacetime.
• Figure 4: Variation of the theoretical shadow radius $R_{\mathrm{sh}}$ for an observer located at $r_O = 100 M$ with $\ell_p = 500 M$: (a) as a function of $Q$ for fixed $a = 0.1 M$, and (b) as a function of $a$ for fixed $Q = 0.2 M$. The dashed blue circle represents the shadow radius of the Schwarzschild–AdS black hole, corresponding to $a = Q = 0$, for which $R_{\mathrm{sh}}^{\mathrm{SAdS}} = 5.248 M$. The central dark disk indicates the limiting configuration reached as the parameters attain larger values.
• Figure 5: Comparison between the theoretical shadow diameter of the charged SV-AdS black hole and the EHT observations of (top row) M87* and (bottom row) Sgr A*, assuming $\ell_p = 1.65 \times 10^{26}\,\mathrm{m}$, corresponding to $\Lambda = -1.1 \times 10^{-52}\,\mathrm{m}^{-2}$. In the left panels, both parameters $a$ and $Q$ are varied simultaneously, whereas in the right panels the parameter $a$ is fixed and the dependence on $Q$ is displayed explicitly. For M87*, the yellow dashed line in the left panel marks the value $d_{\mathrm{sh}} = 9.5$, which corresponds to $Q \simeq \pm 0.681\,M$ and coincides with the point where the black curve in the right panel intersects the $-1\sigma$ boundary of the observational confidence interval. For Sgr A*, the yellow dashed line in the left panel indicates $d_{\mathrm{sh}} = 8.1$, while the solid black line corresponds to $d_{\mathrm{sh}} = 9.5$. These values translate to $Q \simeq \pm 0.987\,M$ and $Q \simeq \pm 0.681\,M$, respectively, marking the intersections of the theoretical curve with the $-1\sigma$ bound and the central observational value in the right panel.