Quantization of Gravity in the Black Hole Background

Abstract

We perform a covariant (Lagrangian) quantization of perturbative gravity in the background of a Schwarzschild black hole. The key tool is a decomposition of the field into spherical harmonics. We fix Regge-Wheeler gauge for modes with angular momentum quantum number $l\ge 2$, while for low multipole modes with $l$ $=$ $0$ or $1$ -- for which Regge-Wheeler gauge is inapplicable -- we propose a set of gauge fixing conditions which are 2D background covariant and perturbatively well-defined. We find that the corresponding Faddeev-Popov ghosts are non-propagating for the $l\ge 2$ modes, but are in general nontrivial for the low multipole modes with $l=0,1$. However, in Schwarzschild coordinates, all time derivatives acting on the ghosts drop from the action and the low multipole ghosts have instantaneous propagators. Up to possible subtleties related to quantizing gravity in a space with a horizon, Faddeev's theorem suggests the possibility of an underlying canonical (Hamiltonian) quantization with a manifestly ghost-free Hilbert space.

29 p

References in corpus (1)

• The Asymptotic Behavior of Massless Fields and the Memory Effect

Cited by in corpus (1)

• Quantization of Gravity in Spherical Harmonic Basis