Killing spinors and spin- fields in type-D spacetimes

Abstract

It is shown that if the background spacetime is a type-D solution of the Einstein vacuum-field equations with cosmological constant or of the Einstein - Maxwell field equations without cosmological constant, an operator can be constructed that maps a solution of the Rarita - Schwinger equation into another solution. In the case of the spin- fields in a type-D electrovac spacetime, we show that the maximal spin weight components, which obey separable decoupled equations, satisfy certain differential relations that are equivalent to the Teukolsky - Starobinsky identities fulfilled by the separated functions. It is also shown that the real and imaginary parts of the Starobinsky constants can be obtained from these relations.