Constraints on the Generalized Uncertainty Principle from black-hole thermodynamics

Abstract

In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions due to the Generalized Uncertainty Principle (GUP). We use the fact that the leading-order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of the GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading-order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading-order corrections to the entropy of a black hole.