Generalized uncertainty principle and asymptotically safe gravity

Abstract

We present a procedure to link the deformation parameter $\beta$ of the generalized uncertainty principle (GUP) to the two free parameters $\om$ and $\gamma$ of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program. To this aim, we compute the Hawking temperature of a black hole in two different ways. The first way involves the use of the GUP in place of the Heisenberg uncertainty relations, and therefore we get a deformed Hawking temperature containing the parameter $\beta$. The second way involves the deformation of the Schwarzschild metric due to the Newtonian coupling constant running according to the AS gravity prescription. The comparison of the two techniques yields a relation between $\beta$ and $\om$, $\gamma$. As a particular case, we discuss also the so called $\xi$-model. The relations between $\beta$ and $\om$, $\xi$ allow us to transfer upper bounds from one parameter to the others.