Quantum Oppenheimer-Snyder black hole evaporation and its fate

TL;DR

This work analyzes Hawking evaporation of a quantum Oppenheimer-Snyder black hole within a semiclassical framework that includes loop quantum gravity corrections via a modified exterior metric with $F(r)=1-2M/r+α M^2/r^4$. By treating a massless scalar field as a test field, it derives the minimally and non-minimally coupled equations, computes greybody factors in the low-frequency limit, and evaluates the resulting emission rates. The key results show that LQG corrections slow and eventually halt evaporation, forming a stable black-hole remnant, with the fate depending on the non-minimal coupling: remnant formation occurs for ξ=-1 but not for ξ=1. Quasi-normal mode analyses corroborate the stability of these remnants, suggesting a possible pathway to resolving the information paradox, though caveats about the Hawking temperature formula and Planck-scale effects remain and warrant further quantum-gravity treatment.

Abstract

In this paper, we investigate the evaporation of the quantum Oppenheimer-Snyder black hole. Within a semiclassical framework, we compute the energy emission of Hawking radiation by introducing a massless scalar field as a test field, considering both minimally and non-minimally coupled cases. For the minimally coupled case, we find that loop quantum gravity effects become crucial at the late stage of the evaporation process, causing the emission rate to slow down and eventually terminate, leading to the formation of a black hole remnant. A quasi-normal mode analysis indicates the stability of this remnant. For the non-minimally coupled case, we show that the fate of the black hole strongly depends on the value of the coupling constant $ξ$. Focusing on the cases $ξ=\pm1$, we find that for $ξ=1$, the energy emission rate accelerates at late times and no remnant is formed, whereas for $ξ=-1$, the emission rate slows down and eventually terminates, resulting in a stable black hole remnant, as supported by the corresponding quasi-normal mode analysis.

Figures (5)

• Figure 1: Comparison of the Hawking radiation emission rate between the classical Schwarzschild black hole and the q-OS black hole with a minimally coupled scalar field.
• Figure 2: $\alpha \in[0.001,0.01]$. The blue dots represent $M_{\text{sol}}$. The orange dots represent $M_{r}$. The green dots represent $M_{\text{final}}$. The red dots represent $M_{\text{min}}$.
• Figure 3: The QNMs for the q-OS BH with a minimally coupled scalar field. $\alpha=0.001$, $M\in[0.1,10.0]$.
• Figure 4: The energy emission rate of the q-OS BH with non-minimally coupled scalar field. The parameter $\alpha=0.001$.
• Figure 5: The QNMs of the q-OS BH with non-minimal scalar with the case of $\xi=-1$. $\alpha=0.001$, $M\in[0.1,10.0]$.