The variance of the Schwarzschild horizon area in linearized quantum gravity is computed to be ~ r_H^2 l_P^2, giving a standard deviation ∆A ~ r_H l_P.
Quantization of Gravity in Spherical Harmonic Basis
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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.
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Quantum uncertainty in the area of a black hole
The variance of the Schwarzschild horizon area in linearized quantum gravity is computed to be ~ r_H^2 l_P^2, giving a standard deviation ∆A ~ r_H l_P.