Gravitational perturbations of type-D vacuum space–times with cosmological constant

Abstract

It is shown that in a type-D vacuum space–time with cosmological constant, the maximal spin weight components of the Weyl spinor perturbations, 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.