Separability of the Dirac equation in a class of perfect fluid space-times with local rotational symmetry

Abstract

Chandrasekhar's technique for separation of the Dirac equation in the Kerr background is applied to perfect fluid space-times with local rotational symmetry. These space-times fall into three distinct types. It is found that in case (1) the Dirac equation separates if the space-time is at least ``locally static'' while in case (3) it separates if the space-time is at least ``locally diagonal,'' in contrast to the massless case where Dhurandhar, Vishveshwara, and Cohen showed that the Hertz potential is separable in all cases. In case (2), however, the Dirac equation is separable in all those cases where the Hertz potential for neutrinos is separable.