The Black Hole Quantum Entropy and Its Minimal Value

TL;DR

This paper shows that black hole quantum entropy, calculated with the Generalized Uncertainty Principle, has a nonzero minimum value related to a minimal length, aligning with holographic principles and previous research.

Contribution

It introduces a new minimal entropy value for Schwarzschild black holes based on the GUP and minimal length assumptions, extending prior theoretical frameworks.

Findings

Black hole entropy has a nonzero minimum under GUP.

The minimal entropy relates to twice the minimal length.

Results are consistent with holographic principles.

Abstract

In the paper it is demonstrated that the Schwarzschild black-hole quantum entropy computed within the scope of the Generalized Uncertainty Principle has a nonzero minimum under the assumption that for a radius of the black hole the lower limit is placed, whose value is twice the minimal length. Such a limit is quite natural when using, as a proper deformation parameter in a quantum theory with a minimal length, the dimensionless small parameter introduced previously by one of the authors in co-authorship with his colleagues and caused by modification of the density matrix at Planck scales. The results obtained have been compared to the results of other authors and analyzed from the viewpoint of their compatibility with the well-known facts and the holographic principle in particular.