Corrections to the Cardy-Verlinde formula from the modified dispersion relation in extra dimensions

TL;DR

This paper investigates how quantum gravity-inspired modified dispersion relations in extra dimensions alter black hole thermodynamics and the Cardy-Verlinde formula, proposing a redefinition of key conformal field theory parameters.

Contribution

It derives corrections to the Schwarzschild black hole thermodynamics and modifies the Cardy-Verlinde formula using the extra dimensional form of the modified dispersion relation.

Findings

Corrections to black hole thermodynamics are obtained.

The Cardy-Verlinde formula is modified accordingly.

Redefinitions of Virasoro operator and central charge account for these corrections.

Abstract

The modified dispersion relation as a common feature of all quantum gravity scenarios provides a perturbation framework upon which the black hole thermodynamics can be corrected. In this letter, we obtain the corrections to the $d$-dimensional Schwarzschild black hole thermodynamics by utilizing the extra dimensional form of the modified dispersion relation, leading to the modification of the Cardy-Verlinde formula. Furthermore, we show that the modified dispersion relation corrections to the Cardy-Verlinde formula can be taken into account by redefining the Virasoro operator and the central charge.