Quantum Oppenheimer-Snyder models in loop quantum cosmology with Lorentz term

TL;DR

This paper develops a quantum black hole model within loop quantum cosmology incorporating the Lorentzian term, revealing modified near-horizon geometry, stability against perturbations, and altered thermodynamic behavior with quantum corrections.

Contribution

It introduces a novel quantum Oppenheimer-Snyder model with Lorentzian term in loop quantum cosmology, showing significant modifications to black hole stability, thermodynamics, and near-horizon geometry.

Findings

Quantum-corrected metric deforms Schwarzschild solution.

Black holes exhibit stability against scalar perturbations.

Quantum corrections lead to phase transitions in heat capacity.

Abstract

A novel quantum black hole model is derived by incorporating the Lorentzian term within the loop quantum cosmology framework of the quantum Oppenheimer-Snyder (qOS) model. This model features a quantum-corrected metric tensor, representing a deformation of the classical Schwarzschild solution. Investigations into the quasi-normal modes reveal that these quantum-corrected black holes exhibit stability against scalar perturbations. Notably, the exponential decay rate within the Lorentzian qOS model demonstrates a significant reduction compared to both the earlier qOS model devoid of this term and the standard Schwarzschild black hole. The higher overtones of the Lorentzian qOS model also differ significantly from those of the earlier qOS model and the standard Schwarzschild black hole, indicating that the near-horizon geometry is substantially modified. The thermodynamic properties with both positive and negative cosmological constant are considered. For the anti-de Sitter case, our analysis reveals that for small black hole masses, the temperature within this loop quantum gravity framework decreases as the mass diminishes, contrasting with classical black hole behavior. Furthermore, a logarithmic term emerges as the leading-order correction to the Bekenstein-Hawking entropy. Additionally, LQG corrections induce an extra phase transition in the black hole's heat capacity at smaller radius. While for the de Sitter case, the temperature increases as the mass decreases for small black holes, again differing from classical expectations. Similarly to the anti-de Sitter case, LQG corrections in the de Sitter case also lead to an extra phase transition in the heat capacity at small radius.