From the Schwarzschild Anti de Sitter Black Hole to the Conformal Field Theory

TL;DR

This paper explores how rainbow gravity modifies the thermodynamics of Schwarzschild anti de Sitter black holes and the resulting corrections to the Cardy-Verlinde formula, linking quantum gravity effects to conformal field theories.

Contribution

It introduces a novel correction to black hole thermodynamics due to rainbow gravity and derives the modified Cardy-Verlinde formula through redefinitions of key conformal field theory parameters.

Findings

Rainbow gravity induces corrections to black hole thermodynamics.

Modified thermodynamics leads to a corrected Cardy-Verlinde formula.

Corrections can be obtained by redefining Virasoro operator and central charge.

Abstract

The emergence of the quantum gravitational effects in a very high energy regime necessitates some corrections to the thermodynamics of Black holes. In this letter, we investigate a possible modification to the thermodynamics of Schwarzschild anti de Sitter (SAdS) black holes due to rainbow gravity model. Using the correspondence between a $(d+1)-$dimensional SAdS black hole and a conformal filed theory in $d$-dimensional spacetime, one may find the corrections to the Cardy-Verlinde formula from the modified thermodynamics of the black hole. Furthermore, we show that the corrected Cardy-Verlinde formula can also be derived by redefining the Virasoro operator and the central charge.