  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.
