Constraints on the Generalized Uncertainty Principle from Black Hole Thermodynamics

TL;DR

This paper investigates how different forms of the Generalized Uncertainty Principle (GUP) affect black hole thermodynamics across various dimensions, constraining GUP models based on entropy correction consistency.

Contribution

It identifies specific GUP forms that produce correct entropy corrections in different dimensions, linking GUP structure to black hole thermodynamics.

Findings

In six dimensions, the usual GUP yields correct entropy corrections.

In five and seven dimensions, a linear GUP is required for correct corrections.

A new GUP with quadratic and cubic momentum terms also matches entropy corrections in five dimensions.

Abstract

In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of 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 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.