Exact solutions of three dimensional black holes: Einstein gravity vs F(R) gravity

TL;DR

This paper derives exact black hole solutions in three-dimensional Einstein and F(R) gravity, analyzing their thermodynamics and conserved quantities to deepen understanding of lower-dimensional gravitational models.

Contribution

It provides new exact solutions for black holes in (2+1)-dimensional Einstein-PMI and F(R) gravity, including thermodynamic analysis and first law validation.

Findings

Exact black hole solutions in Einstein-PMI gravity.

Exact solutions in pure F(R) and conformally invariant Maxwell F(R) gravity.

Validation of thermodynamic laws for these black holes.

Abstract

In this paper, we consider Einstein gravity in the presence of a class of nonlinear electrodynamics, called power Maxwell invariant (PMI). We take into account $(2+1)$-dimensional spacetime in Einstein-PMI gravity and obtain its black hole solutions. Then, we regard pure $F(R)$ gravity as well as $F(R)$-conformally invariant Maxwell theory to obtain exact solutions of the field equations with black hole interpretation. Finally, we investigate the conserved and thermodynamic quantities and discuss about the first law of thermodynamics for the mentioned gravitational models.