Three dimensional dilatonic gravity's rainbow: exact solutions

TL;DR

This paper explores exact three-dimensional dilatonic black hole solutions within gravity's rainbow framework, analyzing their thermodynamic properties, stability, and potential links to dark energy and string theory.

Contribution

It introduces two novel classes of solutions—polynomial and logarithmic—in dilatonic gravity's rainbow and examines their thermodynamic behavior and stability.

Findings

One class is thermally stable, the other unstable.

Conserved and thermodynamic quantities are explicitly calculated.

First law of thermodynamics holds for both classes.

Abstract

Deep relations of dark energy scenario and string theory results into dilaton gravity, on one hand, and the connection between quantum gravity with gravity's rainbow, on the other hand, motivate us to consider three dimensional dilatonic black hole solutions in gravity's rainbow. We obtain two classes of the solutions which are polynomial and logarithmic forms. We also calculate conserved and thermodynamic quantities, and examine the first law of thermodynamics for both classes. In addition, we study thermal stability and show that one of the classes is thermally stable while the other one is unstable.