Screened Simpson-Visser Black Holes with Asymptotically de-Sitter Core

Abstract

In this work, we introduce a screened Simpson-Visser regular solution and perform a comprehensive study of its physical and observational properties. We begin by analyzing the thermodynamic behavior of the black hole, including detailed investigations of the Hawking temperature, Gibbs free energy, and specific heat, which provide insights into its stability and phase structure. Next, we examine the geodesic structure of the spacetime, considering both massless (photon) and massive (timelike) particles. In particular, we study the photon sphere, the corresponding black hole shadow, and the innermost stable circular orbits (ISCO), which are crucial for understanding the motion of matter and light around the black hole. Furthermore, we explore the black hole's energy-emission rate radiation, highlighting the effects of the modified geometry on observational signatures. Finally, we investigate the topological aspects of the black hole, analyzing both the thermodynamic topology and the photon sphere's topological properties. Our analysis demonstrates the intricate interplay between the spacetime geometry, geodesic motion, and black hole thermodynamics, offering a deeper understanding of this class of regular black holes and their potential observational consequences.

Figures (21)

• Figure 1: Behavior of the metric function $A(r)$ as a function of $r/M$ for four representative parameter combinations: $(a/M, \eta/M) = (0.0, 0.5)$ (red solid), $(0.5, 0.0)$ (blue dashed), $(0.5, 0.5)$ (green dash-dot), and the standard Schwarzschild case $(0.0, 0.0)$ (black dotted). The regularization parameter $a$ removes the central singularity, replacing it with a regular wormhole-like core, while the screening parameter $\eta$ exponentially suppresses the gravitational potential at all radii. The combined effect of the two parameters shifts the horizon inward and raises the metric function at the origin. All curves approach $A(r) \to 1$ at spatial infinity, confirming asymptotic flatness.
• Figure 2: Effective refractive index $n(r)$ as a function of $r/M$ for the same four parameter combinations shown in Fig. \ref{['fig:1']}. At large distances $n(r)\to 1$, recovering flat-space optics. Near the event horizon, $n(r)$ diverges, marking the location where the coordinate speed of light vanishes. The screening parameter $\eta$ displaces the divergence to smaller radii, while the regularization parameter $a$ softens the near-horizon slope. The combination of the two parameters yields the smallest effective horizon radius (green dash-dot curve).
• Figure 3: Behavior of the metric function near the origin. Here $a/M=0.1,\,\eta/M=0.2$.
• Figure 4: Behavior of the mass profile $m(r)$ as a function of the dimensionless radial distance for various $a$ and $\eta$.
• Figure 5: Behavior of the density profile $\rho(r)$ near the origin. Here $a/M=0.1,\,\eta/M=0.2$.