F(R) gravity's rainbow and its Einstein counterpart

TL;DR

This paper explores charged black hole solutions and $F(R)$ gravity's rainbow models with energy-dependent geometries, analyzing their properties, thermodynamics, and stability to extend understanding of high-energy modifications to general relativity.

Contribution

It introduces new charged black hole and $F(R)$ gravity's rainbow solutions, comparing geometrical and thermodynamical properties in energy-dependent frameworks.

Findings

Derived energy-dependent black hole solutions with Maxwell sources.

Analyzed thermodynamical behavior and stability of the solutions.

Compared geometrical properties of different $F(R)$ gravity's rainbow models.

Abstract

Motivated by UV completion of general relativity with a modification of a geometry at high energy scale, it is expected to have an energy dependent geometry. In this paper, we introduce charged black hole solutions with power Maxwell invariant source in the context of gravity's rainbow. In addition, we investigate two classes of $F(R)$ gravity's rainbow solutions. At first, we study energy dependent $F(R)$ gravity without energy momentum tensor, and then we obtain $F(R)$ gravity's rainbow in the presence of conformally invariant Maxwell source. We study geometrical properties of the mentioned solutions and compare their results. We also give some related comments regarding to thermodynamical behavior of the obtained solutions and discuss thermal stability of the solutions.