DIRAC-EQUATION IN SOME HOMOGENEOUS SPACE-TIMES, SEPARATION OF VARIABLES AND EXACT-SOLUTIONS

In this article, by the use of a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting differential operators. After separation of variables, the Dirac equation is reduced to a set of coupled ordinary differential equations and some exact solutions corresponding to cosmological backgrounds and gravitational waves are computed in terms of hypergeometric functions. The Klein-Gordon equation in this background field is also discussed.