General analysis of self-dual solutions for the Einstein-Maxwell-Chern-Simons theory in (1+2) dimensions

TL;DR

This paper derives a general solution for the Einstein-Maxwell-Chern-Simons theory in (1+2) dimensions under self-duality, linking a single function to the spacetime geometry and conserved quantities.

Contribution

It provides a closed-form, self-dual solution characterized by a single function, enabling direct computation of physical quantities in (1+2)-dimensional gravity.

Findings

Solution expressed by a single function related to angular momentum

Explicit formulas for total mass and angular momentum

Complete characterization of spacetime geometry

Abstract

The solutions of the Einstein-Maxwell-Chern-Simons theory are studied in (1+2) dimensions with the self-duality condition imposed on the Maxwell field. We give a closed form of the general solution which is determined by a single function having the physical meaning of the quasilocal angular momentum of the solution. This function completely determines the geometry of spacetime, also providing the direct computation of the conserved total mass and angular momentum of the configurations.