Generalized uncertainty principle and Asymptotic Safe gravity

Understand

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.