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C"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Explicit example, where the Hawking temperature of a black hole horizon is compatible with the black hole\u2019s R\u00e9nyi entropy thermodynamic description, is constructed. It is shown that for every static, spherically symmetric, vacuum black hole space-time, a corresponding black hole solution can be derived, where the Hawking temperature is identical with the R\u00e9nyi temperature, i.e.\u00a0the one obtained from the R\u00e9nyi entropy of the black hole via the <jats:italic>1st law<\/jats:italic> of thermodynamics. In order to have this Hawking\u2013R\u00e9nyi type thermodynamic property, the black holes must be surrounded by an anisotropic fluid in the form of a Kiselev metric, where the properties of the fluid are uniquely determined by the mass of the black hole, <jats:italic>M<\/jats:italic>, and the R\u00e9nyi parameter, <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\lambda $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. In the simplest Schwarzschild scenario, the system is found to be thermodynamically unstable, and the <jats:italic>3rd law<\/jats:italic> of thermodynamics seems to play the role of a cosmic censor via placing an upper bound on the black hole\u2019s mass, by which preventing the black hole from loosing its horizon(s).\n<\/jats:p>","DOI":"10.1140\/epjc\/s10052-025-14117-w","type":"journal-article","created":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T20:33:31Z","timestamp":1745267611000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Hawking\u2013R\u00e9nyi black hole thermodynamics, Kiselev solution, and cosmic censorship"],"prefix":"10.1140","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1693-3142","authenticated-orcid":false,"given":"Viktor G.","family":"Czinner","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05jk51a88","id-type":"ROR","asserted-by":"publisher"}],"name":"Nihon University"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5322-4062","authenticated-orcid":false,"given":"Hideo","family":"Iguchi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05jk51a88","id-type":"ROR","asserted-by":"publisher"}],"name":"Nihon University"}]}],"member":"297","published-online":{"date-parts":[[2025,4,21]]},"reference":[{"key":"14117_CR1","doi-asserted-by":"publisher","first-page":"2333","DOI":"10.1103\/PhysRevD.7.2333","volume":"7","author":"JD Bekenstein","year":"1973","unstructured":"J.D. 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