Some exact solutions of Einstein-Dirac-Maxwell fields and massive neutrino

Abstract

Some exact solutions of Einstein-Dirac-Maxwell equations are presented for a zero-mass neutrino. It is found that, in the presence of an electromagnetic field, even the time-dependent Dirac field has ghost solutions. But the solution becomes "ghost-free" in the presence of (charged) matter. It is shown that the time-independent Dirac field has a ghost-free solution if, in the context of the current speculations, the neutrinos are considered to possess some mass.