Black hole thermodynamics in Snyder phase space

Abstract

By defining a noncommutative symplectic structure, we study thermodynamics of Schwarzschild black hole in a Snyder noncommutative phase space for the first time. Since natural cutoffs are the results of compactness of symplectic manifolds in phase space, the physics of black holes in such a space would be affected mainly by these cutoffs. In this respect, this study provides a basis for more deeper understanding of the black hole thermodynamics in a pure mathematical viewpoint.