Energy and Momentum Distributions of the Magnetic Solution to (2+1) Einstein-Maxwell Gravity

TL;DR

This paper calculates the energy and momentum distributions of a magnetic solution in (2+1)-dimensional Einstein-Maxwell gravity using Moeller's energy-momentum complex, providing insights into magnetic fields in lower-dimensional gravity.

Contribution

It explicitly evaluates energy-momentum distributions for a magnetic solution in (2+1) Einstein-Maxwell gravity, a novel application of Moeller's complex in this context.

Findings

Energy and momentum densities are explicitly derived.

The magnetic solution describes a radial magnetic field in AdS background.

The results enhance understanding of energy-momentum in lower-dimensional magnetic spacetimes.

Abstract

We use Moeller's energy-momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein-Maxwell equations. The magnetic spacetime under consideration is a one-parametric solution describing the distribution of a radial magnetic field in a three-dimensional AdS background, and representing the superposition of the magnetic field with a 2+1 Einstein static gravitational field.