Quantization of Gravity in Spherical Harmonic Basis

Abstract

We perform canonical quantization of gravity in the background of a Schwarzschild black hole in the generalized Regge-Wheeler gauge proposed in \cite{Kallosh:2021ors}. 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.

arXiv comment13 p

References in corpus (2)

• Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism
• Quantization of Gravity in the Black Hole Background

Cited by in corpus (3)

• $2\to 2N$ scattering: Eikonalisation and the Page curve
• Off-shell duality invariance of Schwarzschild perturbation theory
• All near-horizon symmetries of the Schwarzschild black hole in linearised gravity