Thermodynamics and shadow of Simpson-Visser black hole with phantom global monopoles

TL;DR

This work analyzes a non-rotating Simpson-Visser black hole endowed with a phantom global monopole, introducing a bounce parameter $a$, symmetry-breaking scale $η$, and coupling $ξ$. By deriving the metric, curvature invariants, and horizon structure, the authors establish the regularity of the spacetime and examine how $a$ and the monopole type modify thermodynamic quantities such as the Hawking temperature $T$, entropy $S$, Gibbs free energy $G$, and specific heat $C$, revealing a global instability with a single local phase transition. They further compute photon orbits and the shadow, obtaining the photon-sphere radius $r_{ph}= frac{3M}{1-8πξη^{2}}$ in the appropriate limit and the shadow radius $R_s= frac{3\sqrt{3}M}{1-8πξη^{2}}$, noting that the critical impact parameter is independent of $a$ and that the phantom monopole yields asymmetric effects relative to the ordinary case. Overall, the bounce parameter $a$ and phantom/global monopole influence horizon structure, thermodynamics, and shadow observables in qualitatively distinct ways from standard Schwarzschild solutions, with potential observational signatures distinguishing phantom from ordinary monopoles. The work also points to future extensions to rotating SV BHs and dark-matter environments as avenues for further study.

Abstract

We investigate the thermodynamics and shadow of a non-rotating Simpson Visser black hole with a phantom global monopole. The model is governed by three parameters: the coupling constant $ξ$, the energy scale of symmetry breaking $η$, and the bounce parameter $a$, which jointly influence horizon structure and observational signatures. Using specific heat and free-energy analysis, we show that small-horizon configurations are locally thermodynamically stable but never globally favored. Analytical solutions of null geodesics reveal that the photon sphere radius depends on the bounce parameter $a$ and the energy scale of symmetry breaking $η$, while the critical impact parameter is still unaffected by $a$. Moreover, the photon sphere radius and critical impact parameter, showing that increasing $η$ enlarges both quantities for an ordinary global monopole, while reducing them in the phantom case. Our results highlight how the bounce parameter and phantom global monopole significantly alter the black hole's physical and geometric properties.

Figures (9)

• Figure 1: A comparison of the metric function $f(r)$ for different BHs as a function of $r$. Here, $a/M=1$, $\eta=0.4$.
• Figure 2: The behavior of the Hawking temperature for the SV BH with PGMs, highlighting the influence of the bounce parameter $a$.
• Figure 3: The behavior of the Hawking temperature for the SV BH with PGMs, highlighting the influence of the energy scale of symmetry breaking parameter $\eta$.
• Figure 4: A comparison of the Gibbs free energy $G$ for different BHs as a function of $r$. Here, $a/M=1$, $\eta=0.4$.
• Figure 5: The behavior of the specific heat for the SV BH with PGMs, highlighting the influence of the bounce parameter $a$.