{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T12:35:05Z","timestamp":1782822905421,"version":"3.54.5"},"reference-count":47,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2024R27"],"award-info":[{"award-number":["PNURSP2024R27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present research note, we discuss the energy\u2013momentum squared gravity model F(R,T2) coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the F(R,T2)-gravity model. Furthermore, we deal with the energy\u2013momentum squared gravity model F(R,T2) coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to F(R,T2)-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schr\u00f6dinger equation for the potential Un with hyperbolic Ricci solitons in the F(R,T2)-gravity model coupled with perfect fluid and a phantom barrier.<\/jats:p>","DOI":"10.3390\/axioms13100708","type":"journal-article","created":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T10:11:04Z","timestamp":1729073464000},"page":"708","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modified F(R,T2)-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1713-6831","authenticated-orcid":false,"given":"Mohd Danish","family":"Siddiqi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2116-7382","authenticated-orcid":false,"given":"Fatemah","family":"Mofarreh","sequence":"additional","affiliation":[{"name":"Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1142\/S0218271800000542","article-title":"The Case for a positive Cosmological Lambda-term","volume":"9","author":"Sahni","year":"2000","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1103\/RevModPhys.75.559","article-title":"The Cosmological Costant and Drak Energy","volume":"75","author":"Peebles","year":"2003","journal-title":"Rev. Mod. 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