CONICET | Buscador de Institutos y Recursos Humanos

For the class of vacuum spacetimes of Petrov type D with cosmological constant (which includes the Kerr-(A)dS solution as a particular case), we show the existence of a general pattern of off shell operator equalities relating linear field equations to decoupled, scalar equations for the spin-weighted components of the fields. The off shell validity allows transposition of operators, which leads to reconstruction formulae for spinor/tensor fields in terms of scalar potentials. We also analyze the role of hidden symmetries associated to Killing spinors and Killing-Yano tensors in the case of spin weight zero. Teukolsky-like equations and Debye potentials previously known are shown to be a particular case of our general results.