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 β 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 β, and therefore we get a deformed Hawking temperature containing the parameter β. The second way involves a deformed Schwarzschild metric containing the Lorentz violating terms s̄^μν of the gravity sector of the SME. The comparison between the two different techniques yields a relation between β and s̄^μν. In this way bounds on β transferred from s̄^μν are improved by many orders of magnitude when compared with those derived in other gravitational frameworks. Also the opposite possibility of bounds transferred from β to s̄^μν is briefly discussed.