{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T01:09:13Z","timestamp":1761268153024,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:00:00Z","timestamp":1761177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["ORF\u20132025-860"],"award-info":[{"award-number":["ORF\u20132025-860"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigate the geometric and physical properties of the h-almost conformal \u03b7-Ricci\u2013Bourguignon soliton and its gradient form by employing a barotropic equation of state within the framework of f(R,T) gravity. We derive this barotropic equation of state under the assumption that the matter content of f(R,T) gravity is modeled by a barotropic perfect fluid. We also examine the way in which these soliton structures both reveal and limit the underlying symmetries of the spacetime geometry. Furthermore, we obtain modified Poisson and Liouville equations associated with these solitons in such a gravitational setting. Additionally, we explore certain harmonic aspects of the h-almost conformal \u03b7-Ricci\u2013Bourguignon soliton on a spacetime filled with a barotropic perfect fluid, considering a harmonic potential function \u03a8. Finally, we present physical interpretations of the conformal pressure p\u02dc in the context of the h-almost conformal \u03b7-Ricci\u2013Bourguignon soliton within f(R,T) gravity.<\/jats:p>","DOI":"10.3390\/sym17111794","type":"journal-article","created":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T00:47:36Z","timestamp":1761266856000},"page":"1794","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["h-Almost Conformal \u03b7-Ricci\u2013Bourguignon Solitons and Spacetime Symmetry in Barotropic Fluids Within f(R,T) Gravity"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6930-3585","authenticated-orcid":false,"given":"Sunil Kumar","family":"Yadav","sequence":"first","affiliation":[{"name":"Department of Applied Science and Humanities, United College of Engineering & Research, UPSIDC, Industrial Area, Naini, Prayagraj 211010, Uttar Predesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3548-4239","authenticated-orcid":false,"given":"Sameh","family":"Shenawy","sequence":"additional","affiliation":[{"name":"Basic Science Department, Modern Academy for Engineering and Technology, Maadi 4411602, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0052-4976","authenticated-orcid":false,"given":"Hanan","family":"Alohali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5638-8655","authenticated-orcid":false,"given":"Carlo","family":"Mantica","sequence":"additional","affiliation":[{"name":"Physics Department Aldo Pontremoli, Universita degli Studi di Milano and I.N.F.N. Sezione di Milano, Via Celoria 16, 20133 Milano, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104016","DOI":"10.1103\/PhysRevD.75.104016","article-title":"Extra force in f(R) modified theories of gravity","volume":"75","author":"Bertolami","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"064036","DOI":"10.1103\/PhysRevD.78.064036","article-title":"Nonminimal coupling of perfect fluids to curvature","volume":"78","author":"Bertolami","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"205002","DOI":"10.1088\/0264-9381\/25\/20\/205002","article-title":"Modified gravity with R\u2013matter couplings and (non-)geodesic motion","volume":"25","author":"Sotiriou","year":"2008","journal-title":"Class. Quantum Grav."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"124040","DOI":"10.1103\/PhysRevD.80.124040","article-title":"Lagrangian description of perfect fluids and modified gravity with an extra force","volume":"80","author":"Faraoni","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.physletb.2012.04.001","article-title":"Interacting agegraphic dark energy model in tachyon cosmology coupled to matter","volume":"711","author":"Farajollahi","year":"2012","journal-title":"Phys. Lett. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1579","DOI":"10.1088\/0264-9381\/10\/8\/017","article-title":"Action functionals for relativistic perfect fluids","volume":"10","author":"Brown","year":"1993","journal-title":"Class. Quantum Grav."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1468","DOI":"10.1103\/PhysRev.94.1468","article-title":"General relativistic variational principle for perfect fluids","volume":"94","author":"Taub","year":"1954","journal-title":"Phys. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2762","DOI":"10.1103\/PhysRevD.2.2762","article-title":"Perfect fluids in general relativity: Velocity potentials and a variational principle","volume":"2","author":"Schutz","year":"1970","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hawking, S.W., and Ellis, G.F.R. (1973). The Large Scale Structure of Space-Time, Cambridge University Press.","DOI":"10.1017\/CBO9780511524646"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1103\/RevModPhys.75.559","article-title":"The cosmological constant and dark energy","volume":"75","author":"Peebles","year":"2003","journal-title":"Rev. Mod. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1142\/S0218271800000542","article-title":"The case for a positive cosmological \u039b-term","volume":"9","author":"Sahni","year":"2000","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.physrep.2004.07.006","article-title":"Dark matter and background light","volume":"402","author":"Overduin","year":"2004","journal-title":"Phys. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1103\/RevModPhys.82.451","article-title":"f(R) theories of gravity","volume":"82","author":"Sotiriou","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physletb.2005.10.010","article-title":"Modified Gauss\u2013Bonnet theory as gravitational alternative for dark energy","volume":"631","author":"Nojiri","year":"2005","journal-title":"Phys. Lett. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106901","DOI":"10.1088\/0034-4885\/79\/10\/106901","article-title":"f(T) teleparallel gravity and cosmology","volume":"79","author":"Cai","year":"2016","journal-title":"Rep. Prog. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Parker, L., and Toms, D.J. (2009). Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, Cambridge University Press.","DOI":"10.1017\/CBO9780511813924"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"024020","DOI":"10.1103\/PhysRevD.84.024020","article-title":"f(R,T)-gravity","volume":"84","author":"Harko","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1086\/156533","article-title":"The stability of a rotating universe","volume":"225","author":"Novello","year":"1978","journal-title":"Astrophys. J."},{"key":"ref_19","unstructured":"O\u2019Neill, B. (1983). Semi-Riemannian Geometry with Applications to Relativity, Academic Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109","DOI":"10.2307\/2373037","article-title":"Harmonic mappings of Riemannian manifolds","volume":"86","author":"Eells","year":"1964","journal-title":"Am. J. Math."},{"key":"ref_21","first-page":"255","article-title":"Three-manifolds with positive Ricci curvature","volume":"17","author":"Hamilton","year":"1982","journal-title":"J. Differ. Geom."},{"key":"ref_22","first-page":"15","article-title":"Conformal Ricci soliton in Kenmotsu manifold","volume":"4","author":"Basu","year":"2015","journal-title":"Glob. J. Adv. Res. Class. Mod. Geom."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/BFb0088841","article-title":"Ricci curvature and Einstein metrics","volume":"Volume 838","author":"Ferus","year":"1981","journal-title":"Global Differential Geometry and Global Analysis (1979 Conference Proceedings)"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"591","DOI":"10.4153\/S0008439520000673","article-title":"Some results on Ricci\u2013Bourguignon solitons and almost solitons","volume":"64","author":"Dwivedi","year":"2021","journal-title":"Can. Math. Bull."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2550067","DOI":"10.1142\/S0219887825500677","article-title":"Relativistic spacetimes admitting h-almost conformal \u03c9-Ricci\u2013Bourguignon solitons","volume":"22","author":"Azami","year":"2025","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Azami, S., De, U.C., and Jafari, M. (2025). Generalized Z-solitons on perfect fluid spacetimes in f(R,T)-gravity. Quaest. Math., 1\u201317.","DOI":"10.2989\/16073606.2025.2543781"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1007\/s13370-022-01025-5","article-title":"Some results on h-almost Ricci\u2013Bourguignon soliton","volume":"33","author":"Azami","year":"2022","journal-title":"Afr. Mat."},{"key":"ref_28","first-page":"341","article-title":"Ricci\u2013Bourguignon solitons and Fischer\u2013Marsden conjecture on generalized Sasakian-space-forms with f-Kenmotsu structure","volume":"60","author":"Chaubey","year":"2023","journal-title":"J. Korean Math. Soc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104578","DOI":"10.1016\/j.geomphys.2022.104578","article-title":"Characterization of general relativistic spacetime equipped with \u03b7-Ricci\u2013Bourguignon soliton","volume":"178","author":"Dey","year":"2022","journal-title":"J. Geom. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2150021","DOI":"10.1142\/S0219887821500213","article-title":"Solitons of K\u00e4hlerian space-time manifolds","volume":"18","author":"Praveena","year":"2021","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_31","unstructured":"Fock, V.A. (1959). The Theory of Space, Time, and Gravitation, Pergamon Press."},{"key":"ref_32","first-page":"440","article-title":"Exact formula for constructing solutions of the Liouville equation \u03942u=ev from solutions of the Laplace equation \u03942v=0","volume":"333","author":"Popov","year":"1993","journal-title":"Dokl. Akad. Nauk"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., and Herlt, E. (2003). Exact Solutions of Einstein\u2019s Field Equations, Cambridge University Press. Cambridge Monographs on Mathematical Physics.","DOI":"10.1017\/CBO9780511535185"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103004","DOI":"10.1103\/PhysRevD.92.103004","article-title":"Cosmology with a stiff matter era","volume":"92","author":"Chavanis","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1088\/0264-9381\/21\/3\/011","article-title":"An introduction to conformal Ricci flow","volume":"21","author":"Fischer","year":"2004","journal-title":"Class. Quantum Grav."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1794\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T01:05:26Z","timestamp":1761267926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1794"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,23]]},"references-count":35,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111794"],"URL":"https:\/\/doi.org\/10.3390\/sym17111794","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,23]]}}}