{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:07:53Z","timestamp":1760058473313,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we investigated the geometric and physical implications of the W3 curvature tensor within the framework of f(R,G) gravity. We found the sufficient conditions for W3 flat spacetimes with constant scalar curvature to be de Sitter (R&gt;0) or Anti-de Sitter (R&lt;0) models. The properties of isotropic spacetime in the modified gravity framework were also investigated. Furthermore, we explored spacetimes with a divergence-free W3 curvature tensor. The necessary and sufficient condition for a W3 Ricci recurrent and parallel spacetime to transform into an Einstein spacetime was determined. Finally, we analyzed the role of the W3 curvature tensor in black hole thermodynamics within f(R,G) gravity.<\/jats:p>","DOI":"10.3390\/sym17040542","type":"journal-article","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T07:47:44Z","timestamp":1743580064000},"page":"542","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of W3 Curvature Tensor in Modified Gravity and Its Cosmological Implications"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8518-4942","authenticated-orcid":false,"given":"Mohabbat","family":"Ali","sequence":"first","affiliation":[{"name":"School of Basic & Applied Sciences, K. R. Mangalam University, Gurugram 122103, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4214-8148","authenticated-orcid":false,"given":"Mohd","family":"Vasiulla","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences & Humanities, Meerut Institute of Engineering & Technology, Meerut 250005, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-1228","authenticated-orcid":false,"given":"Meraj Ali","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, B.-Y. (2011). 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