Asymptotically charged BTZ Black Holes in Gravity's Rainbow

TL;DR

This paper explores three-dimensional charged BTZ black holes within gravity's rainbow framework, analyzing their thermodynamics, stability, and effects of different electrodynamics models, linking quantum gravity effects to black hole properties.

Contribution

It introduces new rainbow black hole solutions incorporating linear and nonlinear electrodynamics, and studies their thermodynamic stability and quantum gravity implications.

Findings

Rainbow black holes are thermally stable.

Electrodynamics models influence black hole thermodynamics.

Quantum gravity effects are encoded in the rainbow functions.

Abstract

Motivated by the wide applications of BTZ black holes and interesting results of gravity's rainbow, we consider three dimensional rainbow solutions and investigate their thermodynamic properties. In addition to investigate black holes thermodynamics related to AdS/CFT correspondence, one may regard gravity's rainbow to to encode quantum gravity effects into the black hole solutions. We take into account the various models of linear and nonlinear electrodynamics and study their effects on the gravity's rainbow spacetime. We also examine thermal stability and find that obtained three dimensional rainbow black holes are thermally stable.