The Spacetime of a Dirac Fermion

TL;DR

This paper provides an approximate, axisymmetric, time-dependent solution to the Einstein-Dirac equations, modeling a massive fermion with its gravitational field and analyzing its conserved quantities.

Contribution

It introduces a novel approximate solution to the Einstein-Dirac equations describing a fermion with self-gravity, expanding understanding of fermionic matter in curved spacetime.

Findings

Solution describes a massive fermion with its gravitational field

Metric approaches flat spacetime at infinity

Conserved quantities have been calculated

Abstract

We present an approximate solution to the minimally coupled Einstein-Dirac equations. We interpret the solution as describing a massive fermion coexisting with its own gravitational field. The solution is axisymmetric but is time dependent. The metric approaches that of a flat spacetime at the spatial infinity. We have calculated a variety of conserved quantities in the system.