Canonical quantization of Teukolsky fields on Kerr backgrounds

Abstract

Electromagnetic and gravitational perturbations on Kerr spacetime can be reconstructed from solutions to the Teukolsky equations. We study the canonical quantization of solutions to these equations for any integer spin. Our quantization scheme involves the analysis of the Hertz potential and one of the Newman-Penrose scalars, which must be related via the Teukolsky-Starobinsky identities. We show that the canonical commutation relations between the fields can be implemented if and only if the Teukolsky-Starobinsky constants are positive, which is the case both for gravitational perturbations and Maxwell fields. We also obtain the Hadamard parametrix of the Teukolsky equation, which is the basic ingredient for a local and covariant renormalization scheme for nonlinear observables. We also discuss the relation of the canonical energy of Teukolsky fields to that of gravitational perturbations.