Debye potentials for the massless Dirac equation in algebraically special spacetimes

Philip Charlton

( Department of Mathematics, University of Newcastle, Callaghan NSW 2308, Australia )

Abstract

In a class of algebraically special spacetimes, we show that a solution of a complex scalar wave equation leads to a solution of the massless Dirac equation. The converse is also true. This technique allows us to construct a symmetry operator for the massless Dirac equation using a conformal Killing-Yano tensor.