Low valence Killing spinors in Gödel's Universe

Abstract

Killing tensors have been of interest historically primarily for generating first integrals for the geodesic equation and for their use in finding separable coordinate systems. A related notion, that of Killing spinors, has recently been shown to be important in the study of generalized symmetries of Maxwell's equations. In a given spacetime, the generalized symmetries depend on the existence of Killing spinors of the spacetime of certain valences. The existence of Killing spinors for the curved metric of Gödel's Universe is investigated. There are five (1,1) Killing spinors, 14 (2,2) and five (1,5) Killing spinors of the spacetime, in addition to the unique (0,2) and (0,4) Killing spinors which are exhibited here as well.