A self consistent solution to the Einstein Maxwell Dirac Equations

TL;DR

This paper presents a localized, continuous solution to the Dirac equation in Kerr-Newman spacetime, where the Dirac particle acts as the source of both curvature and electromagnetic field, under specific parameter conditions.

Contribution

It provides a self-consistent, localized solution to the Einstein-Maxwell-Dirac equations in Kerr-Newman spacetime for particular parameter choices.

Findings

Solution is localized and continuous everywhere.

Valid only for specific parameter choices.

The Dirac particle acts as the source of curvature and electromagnetic field.

Abstract

A self consistent solution to Dirac equation in a Kerr Newman space-time with $M^2 > a^2 + Q^2$ is presented for the case when the Dirac particle is the source of the curvature and the electromagnetic field. The solution is localised, continuous everywhere and valid only for a special choice of the parameters appearing in the Dirac equation.