GUP parameter from quantum gravitational effects

The dimensionless deforming parameter of the generalized uncertainty principle is computed from the generalized metric of a curved spacetime. We assume a deformation of the classical metric of General Relativity due to the quantum gravity corrections in order to compute the perturbed Hawking temperature and determine the deformation parameter of the generalized uncertainty principle. A non numerical value is obtained for the deformation parameter that is compared with the previously obtained values and bounds.