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Almost pseudo-Ricci symmetric spacetime solutions in F(R)-gravity

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Abstract

The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes \((\textit{APRS})_4\). We show that a Robertson–Walker spacetime is \((\textit{APRS})_4\) and vice versa under certain condition imposed on its scale factor. Some popular toy models of F(R)-gravity are also studied under the current setting and various energy conditions are investigated.

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References

  1. Adati, T., Miyazawa, T.: On a Riemannian space with recurrent conformal curvature. Tensor (N.S.) 18, 348–354 (1967)

    MathSciNet  MATH  Google Scholar 

  2. Bektas, E., Zengin, F.Ozen: Almost pseudo Ricci symmetric spacetimes. Differ. Geom. Dyn. Syst 21, 34–46 (2019)

    MathSciNet  MATH  Google Scholar 

  3. Capozziello, S., Mantica, C.A., Molinari, L.G.: Cosmological perfect fluids in f(R) gravity. Int. J. Geom. Methods Mod. Phys. 16, 1950008 (2019)

    Article  MathSciNet  Google Scholar 

  4. Capozziello, S., Mantica, C.A., Molinari, L.G.: Cosmological perfect fluids in Gauss–Bonnet gravity. Int. J. Geom. Methods Mod. Phys. 16, 1950133 (2019)

    Article  MathSciNet  Google Scholar 

  5. Capozziello, S., Mantica, C.A., Molinari, L.G.: Cosmological perfect fluids in higher-order gravity. Gen. Relativ. Gravit. 52, 36 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  6. Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Is cosmic speed-up due to new gravitational physics? Phys. Rev. D 70, 043528 (2004)

    Article  ADS  Google Scholar 

  7. Cartan, E.: Sur une classes remarquable d’espaces de Riemannian. Bull. Soc. Math. France 54, 214–264 (1926)

    Article  MathSciNet  Google Scholar 

  8. Chaki, M.C.: On pseudo-Ricci symmetric manifolds. Bulg. J. Phys. 15, 526–531 (1988)

    MathSciNet  MATH  Google Scholar 

  9. Chaki, M.C.: On pseudo symmetric manifolds. Ann. St. Univ. “Al I Cuza” Iasi 33, 53–58 (1987)

    MathSciNet  MATH  Google Scholar 

  10. Chaki, M.C., Gupta, B.: On conformally symmetric spaces. Indian J. Math. 5, 113–295 (1963)

    MathSciNet  MATH  Google Scholar 

  11. Chaki, M.C., Kawaguchi, T.: On almost pseudo Ricci symmetric manifolds. Tensor (N.S.) 68, 10–14 (2007)

    MathSciNet  MATH  Google Scholar 

  12. Chavanis, P.H.: Cosmology with a stiff matter era. Phys. Rev. D 92, 103004 (2015)

    Article  ADS  Google Scholar 

  13. Curiel, E.: A primer on energy conditions. In: Towards a Theory of Spacetime Theories, pp. 43–104. Birkhäuser, New York (2017)

  14. De, U.C., Ghosh, G.C.: On weakly Ricci symmetric spacetime manifolds. Rad. Mat. 13, 93–101 (2004)

    MathSciNet  MATH  Google Scholar 

  15. De, U.C., Pal, P.: On some classes of almost pseudo Ricci symmetric manifolds. Publ. Math. Debrecen 83, 1–2 (2013)

    Article  MathSciNet  Google Scholar 

  16. De, U.C., Gazi, A.K.: On conformally flat almost pseudo Ricci symmetric manifolds. Kyungpook Math. J. 49, 507–520 (2009)

    Article  MathSciNet  Google Scholar 

  17. De, A., Ozgur, C., De, U.C.: On conformally flat almost pseudo-Ricci symmetric spacetimes. Int. J. Theor. Phys. 51, 2878–2887 (2012)

    Article  MathSciNet  Google Scholar 

  18. Sotiriou, T.P., Faraoni, V.: \(f(R)\) theories of gravity. Rev. Mod. Phys. 82, 451–497 (2010)

    Article  ADS  Google Scholar 

  19. Starobinsky, A.A.: A new type of isotropic cosmological models without singularity. Phys. Lett. B 91, 99–102 (1980)

    Article  ADS  Google Scholar 

  20. Tamássy, L., Binh, T.Q.: On weakly symmetric and weakly projectively symmetric Riemannian manifolds. Colloq. Math. Soc. Janos Bolyai 56, 663–670 (1989)

    MATH  Google Scholar 

  21. Tamássy, L., Binh, T.Q.: On weak symmetries of Einstein and Sasakian manifolds. Tensor (N.S.) 53, 140–148 (1993)

    MathSciNet  MATH  Google Scholar 

  22. Walker, A.G.: On Ruse’s space of recurrent curvature. Proc. Lond. Math. Soc. 52, 36–54 (1950)

    Article  MathSciNet  Google Scholar 

  23. Zeldovich, Y.B.: The equation of state of ultrahigh densities and its relativistic limitations, Soviet physics. J. Exp. Theor. Phys. 14, 1143–1147 (1962)

    Google Scholar 

  24. Zeldovich, Y.B.: A hypothesis, unifying the structure and the entropy of the universe. Mon. Not. R. Astron. Soc. 160, 1–3 (1972)

    Article  ADS  Google Scholar 

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Acknowledgements

The authors are grateful to the referees for their valuable suggestions towards the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Jalan Sungai Long, 43000, Cheras, Malaysia

    Avik De

  2. Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Tee-How Loo

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  1. Avik De
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  2. Tee-How Loo
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Correspondence to Avik De.

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The authors were supported in part by the FRGS research grant (Grant No. FP137-2019A).

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De, A., Loo, TH. Almost pseudo-Ricci symmetric spacetime solutions in F(R)-gravity. Gen Relativ Gravit 53, 5 (2021). https://doi.org/10.1007/s10714-020-02775-y

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