New Solutions of the $2+1$ Dimensional Einstein Gravity Coupled to Maxwell Power type Non Linear Electric field with Dilaton field

TL;DR

This paper derives new solutions for 2+1 dimensional Einstein gravity coupled with a nonlinear Maxwell power electric field and a dilaton, including black hole solutions and their properties.

Contribution

It introduces novel exact solutions in 2+1 gravity with nonlinear electromagnetic and dilaton fields, expanding understanding of such coupled systems.

Findings

Existence of black hole solutions with singularities at r=0

Derivation of the Brown-York mass for these black holes

Analysis of metric behavior near singularities

Abstract

New solutions are derived in the $2+1$ gravity which is coupled to $|{\cal F}|^k$ type non-linear electric field in Maxwell Power theory with dilaton field. We obtain consistent solutions in general $k$ case. We also investigate the behavior of the metric function with the space-time singularity. Then, we found some black hole solutions when the space-time has a singular point at $r=0$. Addition, we derive the Brown-York mass when the space-time represents black hole.