{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T23:58:45Z","timestamp":1767139125046,"version":"build-2238731810"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T00:00:00Z","timestamp":1647648000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T00:00:00Z","timestamp":1647648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Continuum Mech. Thermodyn."],"published-print":{"date-parts":[[2022,5]]},"DOI":"10.1007\/s00161-022-01081-z","type":"journal-article","created":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T05:02:21Z","timestamp":1647666141000},"page":"681-695","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Rarefied relativistic polyatomic gases in a gravitational field"],"prefix":"10.1007","volume":"34","author":[{"given":"J. M. S.","family":"Oliveira","sequence":"first","affiliation":[]},{"given":"M. P. Machado","family":"Ramos","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4771-9859","authenticated-orcid":false,"given":"A. J.","family":"Soares","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,19]]},"reference":[{"key":"1081_CR1","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1002\/andp.19113390503","volume":"339","author":"F J\u00fcttner","year":"1911","unstructured":"J\u00fcttner, F.: Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Ann. Phys. 339, 856\u2013882 (1911). https:\/\/doi.org\/10.1002\/andp.19113390503","journal-title":"Ann. Phys."},{"key":"1081_CR2","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1063\/1.1704047","volume":"4","author":"W Israel","year":"1963","unstructured":"Israel, W.: Relativistic kinetic theory of a simple gas. J. Math. Phys. 4, 1163\u20131181 (1963). https:\/\/doi.org\/10.1063\/1.1704047","journal-title":"J. Math. Phys."},{"key":"1081_CR3","volume-title":"The Kinetic Theory of a Relativistic Gas, Unpublished Report","author":"DC Kelly","year":"1963","unstructured":"Kelly, D.C.: The Kinetic Theory of a Relativistic Gas, Unpublished Report. Miami University, Oxford (1963)"},{"key":"1081_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8165-4","volume-title":"The Relativistic Boltzmann Equation: Theory and Applications","author":"C Cercignani","year":"2002","unstructured":"Cercignani, C., Kremer, G.M.: The Relativistic Boltzmann Equation: Theory and Applications. Birkh\u00e4user Verlag, Basel, Switzerland (2002)"},{"key":"1081_CR5","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1063\/1.4769495","volume":"1501","author":"GM Kremer","year":"2012","unstructured":"Kremer, G.M.: The Boltzmann equation in special and general relativity. AIP Conference Proceedings 1501, 160\u2013167 (2012). https:\/\/doi.org\/10.1063\/1.4769495","journal-title":"AIP Conference Proceedings"},{"key":"1081_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/1742-5468\/2013\/04\/P04016","volume":"P04016","author":"GM Kremer","year":"2013","unstructured":"Kremer, G.M.: Relativistic gas in a Schwarzschild metric. J. Stat. Mech. P04016, 1\u201313 (2013). https:\/\/doi.org\/10.1088\/1742-5468\/2013\/04\/P04016","journal-title":"J. Stat. Mech."},{"key":"1081_CR7","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.physa.2013.09.019","volume":"393","author":"GM Kremer","year":"2014","unstructured":"Kremer, G.M.: Diffusion of relativistic gas mixtures in gravitational fields. Physica A 393, 76\u201385 (2014). https:\/\/doi.org\/10.1016\/j.physa.2013.09.019","journal-title":"Physica A"},{"key":"1081_CR8","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1016\/0031-8914(74)90355-3","volume":"74","author":"JL Anderson","year":"1974","unstructured":"Anderson, J.L., Witting, H.R.: A relativistic relaxation-time model for the Boltzmann equation. Physica 74, 466\u2013488 (1974). https:\/\/doi.org\/10.1016\/0031-8914(74)90355-3","journal-title":"Physica"},{"key":"1081_CR9","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1103\/PhysRev.94.511","volume":"94","author":"PL Bhatnagar","year":"1954","unstructured":"Bhatnagar, P.L., Gross, E.P., Krook, M.: A Model for Collision Processes in Gases. Phys. Rev. 94, 511\u2013525 (1954). https:\/\/doi.org\/10.1103\/PhysRev.94.511","journal-title":"Phys. Rev."},{"key":"1081_CR10","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s00161-009-0095-3","volume":"20","author":"S Brull","year":"2009","unstructured":"Brull, S., Schneider, J.: On the ellipsoidal statistical model for polyatomic gases. Continuum Mech. Thermodyn. 20, 489\u2013508 (2009). https:\/\/doi.org\/10.1007\/s00161-009-0095-3","journal-title":"Continuum Mech. Thermodyn."},{"key":"1081_CR11","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1016\/j.aop.2016.12.012","volume":"377","author":"S Pennisi","year":"2017","unstructured":"Pennisi, S., Ruggeri, T.: Relativistic extended thermodynamics of rarefied polyatomic gas. Ann. Phys. 377, 414\u2013445 (2017). https:\/\/doi.org\/10.1016\/j.aop.2016.12.012","journal-title":"Ann. Phys."},{"issue":"012005","key":"1081_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1088\/1742-6596\/1035\/1\/012005","volume":"1035","author":"S Pennisi","year":"2018","unstructured":"Pennisi, S., Ruggeri, T.: A new BGK model for relativistic kinetic theory of monatomic and polyatomic gases. J. Phys. Conf. Ser 1035(012005), 1\u201311 (2018). https:\/\/doi.org\/10.1088\/1742-6596\/1035\/1\/012005","journal-title":"J. Phys. Conf. Ser"},{"issue":"043102","key":"1081_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1063\/1.5012840","volume":"59","author":"S Pennisi","year":"2018","unstructured":"Pennisi, S., Ruggeri, T.: Relativistic Eulerian rarefied gas with internal structure. J. Math. Phys. 59(043102), 1\u201312 (2018). https:\/\/doi.org\/10.1063\/1.5012840","journal-title":"J. Math. Phys."},{"key":"1081_CR14","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/j.aop.2019.03.025","volume":"405","author":"MC Carrisi","year":"2019","unstructured":"Carrisi, M.C., Pennisi, S., Ruggeri, T.: Production terms in relativistic extended thermodynamics of gas with internal structure via a new BGK model. Ann. Phys. 405, 298\u2013307 (2019). https:\/\/doi.org\/10.1016\/j.aop.2019.03.025","journal-title":"Ann. Phys."},{"key":"1081_CR15","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s00161-018-0694-y","volume":"31","author":"MC Carrisi","year":"2019","unstructured":"Carrisi, M.C., Pennisi, S., Ruggeri, T.: Monatomic limit of relativistic extended thermodynamics of polyatomic gas. Continuum Mech. Thermodyn. 31, 401\u2013412 (2019). https:\/\/doi.org\/10.1007\/s00161-018-0694-y","journal-title":"Continuum Mech. Thermodyn."},{"key":"1081_CR16","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.1007\/s00161-019-00857-0","volume":"32","author":"MC Carrisi","year":"2020","unstructured":"Carrisi, M.C., Pennisi, S.: Hyperbolicity of a model for polyatomic gases in relativistic extended thermodynamics. Continuum Mech. Thermodyn. 32, 1435\u20131454 (2020). https:\/\/doi.org\/10.1007\/s00161-019-00857-0","journal-title":"Continuum Mech. Thermodyn."},{"key":"1081_CR17","unstructured":"Chandrasekhar, S.: An Introduction to the Study of Stellar Structure, Chicago, Illinois, The University of Chicago press (1939, Dover editions: 1958, 1967)"},{"key":"1081_CR18","volume-title":"Relativistic Kinetic Theory. Principles and Applications","author":"SR De Groot","year":"1980","unstructured":"De Groot, S.R., Van Leeuven, W.A., Van-Weert, C.G.: Relativistic Kinetic Theory. Principles and Applications. North-Holland Pub. Co., Amsterdam (1980)"},{"key":"1081_CR19","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1103\/PhysRev.58.919","volume":"58","author":"C Eckart","year":"1940","unstructured":"Eckart, C.: The thermodynamics of irreversible processes III. Phys. Rev. 58, 919\u2013924 (1940). https:\/\/doi.org\/10.1103\/PhysRev.58.919","journal-title":"Phys. Rev."},{"key":"1081_CR20","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/BF01332580","volume":"10","author":"A Friedman","year":"1922","unstructured":"Friedman, A.: \u00dcber die Kr\u00fcmmung des Raumes. Z. Phys. 10, 377\u2013386 (1922). https:\/\/doi.org\/10.1007\/BF01332580","journal-title":"Z. Phys."},{"key":"1081_CR21","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1103\/PhysRev.56.455","volume":"56","author":"JR Oppenheimer","year":"1939","unstructured":"Oppenheimer, J.R., Snyder, H.: On continued gravitational contraction. Phys. Rev. 56, 455\u2013459 (1939). https:\/\/doi.org\/10.1103\/PhysRev.56.455","journal-title":"Phys. Rev."},{"key":"1081_CR22","doi-asserted-by":"publisher","first-page":"4862","DOI":"10.1103\/PhysRevD.54.4862","volume":"54","author":"F Fayos","year":"1996","unstructured":"Fayos, F., Senovilla, J.M.M., Torres, R.: General matching of two spherically symmetric spacetimes. Phys. Rev. D 54, 4862\u20134872 (1996). https:\/\/doi.org\/10.1103\/PhysRevD.54.4862","journal-title":"Phys. Rev. D"},{"key":"1081_CR23","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1016\/j.physa.2012.12.006","volume":"392","author":"M Pavi\u0107","year":"2013","unstructured":"Pavi\u0107, M., Ruggeri, T., Simi\u0107, S.: Maximum entropy principle for rarefied polyatomic gases. Physica A 392, 1302\u20131317 (2013). https:\/\/doi.org\/10.1016\/j.physa.2012.12.006","journal-title":"Physica A"},{"key":"1081_CR24","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1007\/s00205-020-01590-8","volume":"239","author":"T Ruggeri","year":"2021","unstructured":"Ruggeri, T., Xiao, Q., Zhao, H.: Nonlinear hyperbolic waves in relativistic gases of massive particles with Synge energy. Arch. Rational Mech. Anal 239, 1061\u20131109 (2021). https:\/\/doi.org\/10.1007\/s00205-020-01590-8. (Continuum Mech. Thermodyn.)","journal-title":"Arch. Rational Mech. Anal"}],"updated-by":[{"DOI":"10.1007\/s00161-022-01104-9","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T00:00:00Z","timestamp":1650326400000}}],"container-title":["Continuum Mechanics and Thermodynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00161-022-01081-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00161-022-01081-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00161-022-01081-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T10:23:27Z","timestamp":1651487007000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00161-022-01081-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,19]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,5]]}},"alternative-id":["1081"],"URL":"https:\/\/doi.org\/10.1007\/s00161-022-01081-z","relation":{},"ISSN":["0935-1175","1432-0959"],"issn-type":[{"value":"0935-1175","type":"print"},{"value":"1432-0959","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,19]]},"assertion":[{"value":"12 October 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2022","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s00161-022-01104-9","URL":"https:\/\/doi.org\/10.1007\/s00161-022-01104-9","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}]}}