{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T20:24:09Z","timestamp":1775161449817,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hearne Institute for Theoretical Physics","award":["NSF-PHY-1903799"],"award-info":[{"award-number":["NSF-PHY-1903799"]}]},{"name":"Hearne Institute for Theoretical Physics","award":["NSF-PHY-2206557"],"award-info":[{"award-number":["NSF-PHY-2206557"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We study the canonical quantization of a scalar field in Kantowski\u2013Sachs 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\u2013Sachs type.<\/jats:p>","DOI":"10.3390\/math11183922","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T03:50:10Z","timestamp":1694749810000},"page":"3922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fock Quantization of a Klein\u2013Gordon Field in the Interior Geometry of a Nonrotating Black Hole"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9705-6769","authenticated-orcid":false,"given":"Jer\u00f3nimo","family":"Cortez","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6242-7814","authenticated-orcid":false,"given":"Beatriz","family":"Elizaga Navascu\u00e9s","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3378-9610","authenticated-orcid":false,"given":"Guillermo A.","family":"Mena Marug\u00e1n","sequence":"additional","affiliation":[{"name":"Instituto de Estructura de la Materia, IEM-CSIC, C\/Serrano 121, 28006 Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0108-1757","authenticated-orcid":false,"given":"\u00c1lvaro","family":"Torres-Caballeros","sequence":"additional","affiliation":[{"name":"Instituto de Estructura de la Materia, IEM-CSIC, C\/Serrano 121, 28006 Madrid, Spain"}]},{"given":"Jos\u00e9","family":"Velhinho","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias and FibEnTech-UBI, Universidade da Beira Interior, R. Marqu\u00eas D\u2019\u00c1vila e Bolama, 6201-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1063\/1.1704952","article-title":"Some spatially inhomogeneous dust models","volume":"7","author":"Kantowski","year":"1966","journal-title":"J. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1063\/1.526935","article-title":"Kantowski\u2013Sachs cosmological models as big-bang models","volume":"26","author":"Weber","year":"1985","journal-title":"J. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1007\/s10773-008-9663-8","article-title":"Kantowski-Sachs cosmological model in general theory of relativity","volume":"47","author":"Adhav","year":"2008","journal-title":"Int. J. Theor. 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