Fock Quantization of a Klein–Gordon Field in the Interior Geometry of a Nonrotating Black Hole

Jerónimo Cortez, Beatriz Elizaga Navascués, Guillermo A. Mena Marugán (), Álvaro Torres-Caballeros and José Velhinho
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Jerónimo Cortez: Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
Beatriz Elizaga Navascués: Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA
Guillermo A. Mena Marugán: Instituto de Estructura de la Materia, IEM-CSIC, C/Serrano 121, 28006 Madrid, Spain
Álvaro Torres-Caballeros: Instituto de Estructura de la Materia, IEM-CSIC, C/Serrano 121, 28006 Madrid, Spain
José Velhinho: Faculdade de Ciências and FibEnTech-UBI, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal

Mathematics, 2023, vol. 11, issue 18, 1-16

Abstract: We study the canonical quantization of a scalar field in 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.

Keywords: quantum fields; Kantowski–Sachs spacetime; unitary dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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