Lorentz violation and generalized uncertainty principle

TL;DR

This paper links the deformation parameter of the generalized uncertainty principle to Lorentz-violating coefficients in the SME by comparing black hole Hawking temperatures, leading to significantly improved bounds on these parameters.

Contribution

It introduces a novel method to relate GUP deformation parameter to SME Lorentz violation coefficients via black hole thermodynamics.

Findings

Bounds on GUP parameter $eta$ are significantly improved.

A relation between $eta$ and SME coefficients $ar{s}^{ ueta}$ is established.

The method enhances constraints on Lorentz violation from gravitational phenomena.

Abstract

Investigations on possible violation of Lorentz invariance have been widely pursued in the last decades, both from theoretical and experimental sides. A comprehensive framework to formulate the problem is the standard model extension (SME) proposed by A.Kostelecky, where violation of Lorentz invariance is encoded into specific coefficients. Here we present a procedure to link the deformation parameter $\beta$ of the generalized uncertainty principle (GUP) to the SME coefficients of the gravity sector. The idea is to compute the Hawking temperature of a black hole in two different ways. The first way involves the deformation parameter $\beta$, and therefore we get a deformed Hawking temperature containing the parameter $\beta$. The second way involves a deformed Schwarzschild metric containing the Lorentz violating terms $\bar{s}^{\mu\nu}$ of the gravity sector of the SME. The comparison between the two different techniques yields a relation between $\beta$ and $\bar{s}^{\mu\nu}$. In this way bounds on $\beta$ transferred from $\bar{s}^{\mu\nu}$ are improved by many orders of magnitude when compared with those derived in other gravitational frameworks. Also the opposite possibility of bounds transferred from $\beta$ to $\bar{s}^{\mu\nu}$ is briefly discussed.