Exact solution of the Dirac equation in the presence of a gravitational instanton

Abstract

We solve the massless Dirac equation in the presence of a Bianchi V II0 instanton metric. In order to separate variables we apply the algebraic method of separation. We express the curved Dirac gamma matrices in a rotating tetrad and compute the corresponding spinor connections. The resulting system of equations is completely decoupled after introducing two new complex space variables. Applying a pairwise separation scheme we also succeed in separating variables in the massless Dirac equation coupled to a Eguchi-Hanson instanton metric. The spinor solutions are expressed in terms of weighted spherical spinors.