{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T04:38:08Z","timestamp":1781239088889,"version":"3.54.1"},"reference-count":155,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,5,14]],"date-time":"2016-05-14T00:00:00Z","timestamp":1463184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["NI 1282\/2-1"],"award-info":[{"award-number":["NI 1282\/2-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum N-portrait beyond the semi-classical limit. We show that for a generic N this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition.<\/jats:p>","DOI":"10.3390\/e18050181","type":"journal-article","created":{"date-parts":[[2016,5,17]],"date-time":"2016-05-17T10:20:11Z","timestamp":1463480411000},"page":"181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Geometric Model of Black Hole Quantum N-portrait, Extradimensions and Thermodynamics"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9937-486X","authenticated-orcid":false,"given":"Antonia","family":"Frassino","sequence":"first","affiliation":[{"name":"Frankfurt Institute for Advandced Studies (FIAS), Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Frankfurt am Main 60438, Germany"},{"name":"Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Frankfurt am Main 60439, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sven","family":"K\u00f6ppel","sequence":"additional","affiliation":[{"name":"Frankfurt Institute for Advandced Studies (FIAS), Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Frankfurt am Main 60438, Germany"},{"name":"Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Frankfurt am Main 60439, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7286-9774","authenticated-orcid":false,"given":"Piero","family":"Nicolini","sequence":"additional","affiliation":[{"name":"Frankfurt Institute for Advandced Studies (FIAS), Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Frankfurt am Main 60438, Germany"},{"name":"Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Frankfurt am Main 60439, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1093\/mnras\/168.2.399","article-title":"Black holes in the early Universe","volume":"168","author":"Carr","year":"1974","journal-title":"Mon. 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