{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T21:22:02Z","timestamp":1768771322295,"version":"3.49.0"},"reference-count":59,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T00:00:00Z","timestamp":1628726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/MAT\/00212\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/00212\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Universe"],"abstract":"<jats:p>The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schr\u00f6dinger\u2019s type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states in this model.<\/jats:p>","DOI":"10.3390\/universe7080297","type":"journal-article","created":{"date-parts":[[2021,8,12]],"date-time":"2021-08-12T22:14:36Z","timestamp":1628806476000},"page":"297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Hawking Radiation and Black Hole Gravitational Back Reaction\u2014A Quantum Geometrodynamical Simplified Model"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3974-9177","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Marto","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade da Beira Interior, Rua Marqu\u00eas D\u2019\u00c1vila e Bolama, 6200-001 Covilh\u00e3, Portugal"},{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es da Universidade da Beira Interior, Rua Marqu\u00eas D\u2019\u00c1vila e Bolama, 6200-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1103\/PhysRevD.14.2460","article-title":"Breakdown of predictability in gravitational collapse","volume":"14","author":"Hawking","year":"1976","journal-title":"Phys. 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