Noncommutative Schwarzschild geometry and generalized uncertainty principle

Abstract

We discuss a possible link between the deformation parameter $$\Theta ^{\mu \nu }$$ arising in the framework of noncommutative geometry and the parameter $$\beta $$ of the generalized uncertainty principle (GUP). We compute the shift of the Hawking temperature induced by the $$\Theta ^{\mu \nu }$$ -deformed Schwarzschild geometry, and then we relate it to one obtained by GUP. Results suggest a granular structure of specetime at the Planck scales. The current bounds on $$\beta $$ allow to constraint the noncommutative parameter $$\Theta ^{\mu \nu }$$ .