GRAVITATIONAL PERTURBATIONS OF TYPE-D VACUUM SPACE-TIMES WITH COSMOLOGICAL CONSTANT

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.