Quantization of Gravity in Spherical Harmonic Basis

TL;DR

This paper presents a canonical quantization of gravity around a Schwarzschild black hole, demonstrating a unitary, ghost-free Hamiltonian with specific degrees of freedom, applicable also in Minkowski space.

Contribution

It introduces a new quantization scheme for gravity in spherical coordinates using the Regge-Wheeler gauge, ensuring unitarity and ghost-freedom at quadratic order.

Findings

Hamiltonian is unitary and ghost-free

Two degrees of freedom linked to metric perturbations

Quantization valid in both black hole and Minkowski backgrounds

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.