# An Application of Lorentz Invariance Violation in Black Hole Thermodynamics

## TL;DR

This paper investigates how Lorentz invariance violation (LIV) affects black hole thermodynamics, revealing accelerated evaporation, modified entropy, and avoidance of singularities, with comparisons to other quantum gravity models like GUP.

## Contribution

It introduces a phenomenological study of LIV-DR effects on black hole thermodynamics, highlighting their impact on evaporation and entropy corrections, and compares them with GUP.

## Key findings

- LIV-DR speeds up black hole evaporation.
- Black hole entropy receives a logarithmic correction.
- LIV-DR effects naturally bypass singularities.

## Abstract

In this paper, we have applied the Lorentz-invariance-violation (LIV) class of dispersion relations (DR) with the dimensionless parameter n = 2 and the "sign of LIV" {\eta}_+ = 1, to phenomenologically study the effect of quantum gravity in the strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the "reduced Bekenstein-Hawking entropy", and the ill defined situations (i.e. the singularity problem and the critical problem) are naturally bypassed when the LIV-DR effect is present. Also, to put our results in a proper perspective, we have compared with the earlier findings by another quantum gravity candidate, i.e. the generalized uncertainty principle (GUP). Finally, we conclude from the inert remnants at the final stage of the black hole evaporation that, the GUP as a candidate for describing quantum gravity can always do as well as the LIV-DR by adjusting the model-dependent parameters, but in the same model-dependent parameters the LIV-DR acts as a more suitable candidate.