Symmetry operators and decoupled equations for linear fields on black hole spacetimes

Understand

In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed {\em off shell} with the Dirac, Maxwell and linearized gravity equations, give a system of equations for spin weighted scalars associated to the linear fields, that decouple on shell.

• Using these operator relations we give compact reconstruction formulae for solutions of the original spinor and tensor field equations in terms of solutions of the decoupled scalar equations.
• We also analyze the role of Killing spinors and Killing-Yano tensors in the spin weight zero equations and, in the case of spherical symmetry, we compare our four-dimensional formulation with the standard $2+2$ decomposition and particularize to the Schwarzschild-(A)dS black hole.
• Our results uncover a pattern that generalizes a number of previous results on Teukolsky-like equations and Debye potentials for higher spin fields.