Magnetic solutions to 2+1 dimensional gravity with dilaton field

TL;DR

This paper presents a general method for solving 2+1 dimensional dilatonic Maxwell-Einstein equations with cosmological constant, identifying solutions with horizons that differ from non-dilatonic cases.

Contribution

It introduces a systematic approach to find solutions in 2+1D dilaton gravity with magnetic fields, revealing new horizon-bearing solutions.

Findings

Some solutions possess horizons unlike non-dilatonic cases

All solutions are static and rotationally symmetric with magnetic and dilaton fields

The method applies to both positive and negative cosmological constants

Abstract

We show a general method to solve 2+1 dimensional dilatonic Maxwell-Einstein equation with a positive or negative cosmological constant. All the physical solutions are listed with assumptions that they are static, rotationally symmetric, and has a nonzero magnetic field and a nonzero dilaton field. On the contrary to the magnetic solution without a dilaton field, some of the present solutions with a dilaton field possess a horizon.