Lorentz violation and generalized uncertainty principle

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 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 (S)over-bar(mu nu) of the gravity sector of the SME. The comparison between the two different techniques yields a relation between beta and (S)over-bar(mu nu). In this way bounds on beta transferred from (S)over-bar(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 (S)over-bar(mu nu) is briefly discussed.