{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T17:59:29Z","timestamp":1762624769244,"version":"build-2065373602"},"reference-count":67,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,19]],"date-time":"2022-01-19T00:00:00Z","timestamp":1642550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric f(R) gravity to carry out our analysis. It is noticed that the matter distribution cannot fill the region close to the center of symmetry, thereby implying the existence of an empty core. Moreover, the evaluation of the effective energy density reveals that it is inevitably negative, which could have utmost relevance in understanding various quantum field events. To derive the structure scalars, we perform the orthogonal splitting of the Riemann tensor in this modified gravity. Few relationships among matter variables and both Tolman and Misner Sharp are determined. Through two generating functions, some hyperbolically symmetric cosmological models, as well as their physical interpretations, are studied. To delve deeply into the role of f(R) terms, the model of the less-complex relativistic system of Einstein gravity is presented.<\/jats:p>","DOI":"10.3390\/e24020150","type":"journal-article","created":{"date-parts":[[2022,1,19]],"date-time":"2022-01-19T08:20:57Z","timestamp":1642580457000},"page":"150","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8227-2621","authenticated-orcid":false,"given":"Z.","family":"Yousaf","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam Campus, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6286-1135","authenticated-orcid":false,"given":"M. Z.","family":"Bhatti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam Campus, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1653-6964","authenticated-orcid":false,"given":"Maxim","family":"Khlopov","sequence":"additional","affiliation":[{"name":"Institute of Physics, Southern Federal University, 194 Stachki, 344090 Rostov-on-Donu, Russia"},{"name":"CNRS, Astroparticule et Cosmologie, Universite de Paris, F-75013 Paris, France"},{"name":"Institute of Nuclear Physics and Engineering, National Research Nuclear University MEPhI, 115409 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Asad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam Campus, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1002\/andp.19053221004","article-title":"Zur elektrodynamik bewegter k\u00f6rper","volume":"4","author":"Einstein","year":"1905","journal-title":"Ann. 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