Thermal fluctuations and greybody factor of loop quantum black holes

Abstract

This research investigates the thermal fluctuations and greybody factor of a (3+1)-dimensional black hole within the framework of loop quantum gravity, incorporating higher-order corrections. Our findings indicate that the event horizons are significantly influenced by the loop quantum black hole parameters causing the event horizon to shift outward from the center. We observe the higher-order corrected entropy and respective physical quantities like internal energy, Helmholtz free energy, and Gibbs free energy are evaluated. It reveals that larger black holes tend to have lower values of corrected energies suggesting greater thermodynamic stability. Using the Klein–Gordon equation transformed into a Schrödinger wave equation via tortoise coordinates, we derive the effective potential and analyze its behavior relative to key parameters, including the black hole parameters, and angular momentum. The effective potential exhibits maximum values at smaller horizon radii, decreasing for more massive black holes, highlighting the complex relationship between mass and horizon structure. By solving the radial equation, we can derive two solutions corresponding to the event and cosmic horizons. Using these two solutions in the intermediate regime, we can ascertain the greybody component and its associated behavior. Additionally, raising the quantum parameter also results in a drop in the rate of absorption, demonstrating that the presence of a quantum parameter lowers the absorption rate of Schwarzschild black hole. These intricate dynamics underscore the significant role of loop quantum gravity parameters in shaping black hole thermodynamics and point to potential avenues for future research into their observational implications.