The Spacetime of a Dirac Fermion

Jianwei Mei

Published 2011-02-18, updated 2011-05-29Version 2

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.