Fock quantization of a Klein-Gordon field in the interior geometry of a nonrotating black hole

TL;DR

This paper develops a unique Fock quantization scheme for a scalar field in a Kantowski-Sachs spacetime, relevant for black hole interiors, ensuring unitarity and symmetry preservation, and clarifies the quantum-classical correspondence.

Contribution

It introduces a canonical transformation approach that isolates background effects, leading to a unique, symmetry-preserving Fock quantization of scalar fields in black hole interior geometries.

Findings

Quantization is unique under unitarity and symmetry conditions.

Canonical transformation helps separate background evolution from quantum dynamics.

Results apply to black hole interiors, extending cosmological quantization methods.

Abstract

We study the canonical quantization of a scalar field in a Kantowski-Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is to a large extent determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski-Sachs type.