Weakly Ricci-Symmetric Space-Times and f ( R, G ) Gravity

Yanlin Li (), Uday Chand De and Krishnendu De
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Uday Chand De: Department of Pure Mathematics, University of Calcutta, Kolkata 700019, West Bengal, India
Krishnendu De: Department of Mathematics, Kabi Sukanta Mahavidyalaya, The University of Burdwan, Bhadreswar 712221, West Bengal, India

Mathematics, 2025, vol. 13, issue 6, 1-15

Abstract: In the present article, we classify conformally flat weakly Ricci-symmetric space-times and obtain that they represent Robertson–Walker space-times. Furthermore, we provethat a Ricci-recurrent weakly Ricci-symmetric space-time is static and a Ricci-semi-symmetric weakly Ricci-symmetric space-time does not exist. Further, we acquire the conditions under which a weakly Ricci-symmetric twisted space-time becomes a generalized Robertson–Walker space-time. Also, we examine the effect of conformally flat weakly Ricci-symmetric space-time solutions in f ( R , G ) gravity by considering two models, and we see that the null, weak and strong energy conditions are verified, but the dominant energy condition fails, which is also consistent with present observational studies that reveal the universe is expanding. Finally, we apply the flat Friedmann–Robertson–Walker metric to deduce a relation between deceleration, jerk and snap parameters.

Keywords: Robertson–Walker space-time; weakly Ricci-symmetric space-time; energy conditions; f ( R , G ) gravity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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