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Quantization of gravity in spherical harmonic basis
Physical Review D  (IF5.296),  Pub Date : 2021-10-19, DOI: 10.1103/physrevd.104.086023
Renata Kallosh

We perform canonical quantization of gravity in the background of a Schwarzschild black hole in the generalized Regge-Wheeler gauge proposed in Kallosh and Rahman [Quantization of gravity in the black hole background, Phys. Rev. D 104, 086008 (2021)]. We find that the Hamiltonian at the quadratic level is unitary and ghost-free. Two canonical degrees of freedom are associated with Zerilli-Moncrief and Cunningham-Price-Moncrief functions of the metric perturbations. The $\ell <2$ part of the Hamiltonian vanishes. This quantization with the unitary Hamiltonian for gravity is valid also in Minkowski space in spherical coordinates.