$(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory

TL;DR

This paper presents an exact static solution for charged black holes with scalar hair in (2+1)-dimensional Einstein-Power-Maxwell theory, analyzing their horizon structure, stability, and geodesic behavior.

Contribution

It provides a new exact solution in Einstein-Power-Maxwell theory with scalar hair in (2+1) dimensions, including stability analysis and geodesic motion classification.

Findings

Existence of black hole solutions with scalar hair and negative mass.

Identification of horizon structures and mass bounds for stability.

Detailed classification of null geodesic motions in the spacetime.

Abstract

We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.