The Generalized Uncertainty Principle and Corrections to the Cardy-Verlinde Formula in $SAdS_5$ Black Holes

TL;DR

This paper explores how string-inspired modifications to the uncertainty principle affect the thermodynamics of 5D AdS black holes and proposes corrected formulas for entropy and the Cardy-Verlinde relation by redefining key parameters.

Contribution

It introduces a method to incorporate generalized uncertainty principle corrections into the Cardy-Verlinde entropy formula through redefinitions of the Virasoro operator and central charge.

Findings

Corrected temperature and entropy for 5D Schwarzschild AdS black holes.

Modified Cardy-Verlinde formula accounting for GUP corrections.

Redefinition of Virasoro operator and central charge to include quantum corrections.

Abstract

In this letter, we investigate a possible modification to the temperature and entropy of $5-$dimensional Schwarzschild anti de Sitter black holes due to incorporating stringy corrections to the modified uncertainty principle. Then we subsequently argue for corrections to the Cardy-Verlinde formula in order to account for the corrected entropy. Then we show, one can taking into account the generalized uncertainty principle corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator $L_0$ and the central charge $c$.