On modified Hawking radiation under quantum gravity effects in the fermion sector

TL;DR

This paper investigates how quantum gravity effects, specifically Lorentz invariance violation, modify Hawking radiation and black hole entropy calculations, emphasizing the importance of consistent dispersion relations and gamma matrix structures.

Contribution

It provides a consistent method to incorporate LIV-induced dispersion relation modifications into Hawking radiation and entropy calculations for static black holes.

Findings

LIV leads to temperature corrections proportional to dispersion relation modifications.

Entropy of Reissner-Nordström and Schwarzschild black holes receives LIV-related corrections.

Ensures consistency between dispersion relations and fermionic gamma matrices in tunneling calculations.

Abstract

In this letter, after briefly discussing the Hawking radiation (HR) as a quantum tunneling, we emphasize that special care must be taken when computing temperature corrections in the presence of Lorentz invariance violation (LIV), particularly by ensuring consistency between the modified dispersion relation and the gamma matrix structure used to describe fermions that are tunneling. We present a consistent implementation of such corrections in static, spherically symmetric black hole (BH) spacetimes. Our results show that introducing terms that increase/decrease the energy in the dispersion relation--originally determined by Lorentz invariance--leads to a corresponding increase/decrease in the Hawking temperature, when the dispersion relation is uniquely determined. We also determined the changes in Bekenstein-Hawking entropy for the Reissner-Nordstr\"om and Schwarzschild BHs, including corrections from LIV scenarios.