Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity
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 do...
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2025-03-01
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| author | Yanlin Li Uday Chand De Krishnendu De |
| author_facet | Yanlin Li Uday Chand De Krishnendu De |
| author_sort | Yanlin Li |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-9e2b416f076b45cd8e4359975c720c75 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-9e2b416f076b45cd8e4359975c720c752025-08-20T02:42:22ZengMDPI AGMathematics2227-73902025-03-0113694310.3390/math13060943Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) GravityYanlin Li0Uday Chand De1Krishnendu De2School of Mathematics, Hangzhou Normal University, Hangzhou 311121, ChinaDepartment of Pure Mathematics, University of Calcutta, Kolkata 700019, West Bengal, IndiaDepartment of Mathematics, Kabi Sukanta Mahavidyalaya, The University of Burdwan, Bhadreswar 712221, West Bengal, IndiaIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/13/6/943Robertson–Walker space-timeweakly Ricci-symmetric space-timeenergy conditions<i>f</i> (<i>R</i>,<i>G</i>) gravity |
| spellingShingle | Yanlin Li Uday Chand De Krishnendu De Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity Mathematics Robertson–Walker space-time weakly Ricci-symmetric space-time energy conditions <i>f</i> (<i>R</i>,<i>G</i>) gravity |
| title | Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity |
| title_full | Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity |
| title_fullStr | Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity |
| title_full_unstemmed | Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity |
| title_short | Weakly Ricci-Symmetric Space-Times and <i>f</i> (<i>R</i>,<i>G</i>) Gravity |
| title_sort | weakly ricci symmetric space times and i f i i r i i g i gravity |
| topic | Robertson–Walker space-time weakly Ricci-symmetric space-time energy conditions <i>f</i> (<i>R</i>,<i>G</i>) gravity |
| url | https://www.mdpi.com/2227-7390/13/6/943 |
| work_keys_str_mv | AT yanlinli weaklyriccisymmetricspacetimesandifiiriigigravity AT udaychandde weaklyriccisymmetricspacetimesandifiiriigigravity AT krishnendude weaklyriccisymmetricspacetimesandifiiriigigravity |