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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

Perfect fluid spacetimes, Gray's decomposition and $f(\mathcal{R}, {T})$-gravity

Sinem Güler(ISTANBUL SABAHATTIN ZAIM UNIVERSITY)0000-0001-9994-2927
U.c. De(CALCUTTA UNIVERSITY)0000-0002-8990-4609
Pages
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Publication Date
2022-02-14
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We find some relations between isotropic pressure and energy density of the Ricci semisymmetric perfect fluid spacetimes satisfying $f(\mathcal{R},T)$-gravity equation to represent dark matter era.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, first we give the complete classifications of perfect fluid spacetimes under the Gray's decomposition.
📊
Key Findings & Data:Then we investigate the condition under which the Ricci tensor is a conformal Killing tensor in a perfect fluid spacetime.
💡
Conclusion & Impact:We find some relations between isotropic pressure and energy density of the Ricci semisymmetric perfect fluid spacetimes satisfying $f(\mathcal{R},T)$-gravity equation to represent dark matter era.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:perfect fluid · Gray's decomposition · $f(\mathcal{R}

Abstract

In this paper, first we give the complete classifications of perfect fluid spacetimes under the Gray's decomposition. Then we investigate the condition under which the Ricci tensor is a conformal Killing tensor in a perfect fluid spacetime. Later, we study perfect fluid spacetimes in $f(\mathcal{R},T)$-gravity theory. We find some relations between isotropic pressure and energy density of the Ricci semisymmetric perfect fluid spacetimes satisfying $f(\mathcal{R},T)$-gravity equation to represent dark matter era.

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Cite This Article

Güler, S., De, U. (2022). Perfect fluid spacetimes, Gray's decomposition and $f(\mathcal{R}, {T})$-gravity. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.927654

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References (45)

  1. G. Abbas, M. S. Khan, Z. Ahmad and M. Zubair, Higher-dimensional inhomogeneous perfect fluid collapse in f(R)-gravity, Eur. Phys. J. C. 77, Article No: 443, 2017.
  2. L.J. Alias, A. Romero and M. Sanchez, Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes, Gen. Relativ. Gravit. 27 (1), 71–84, 1995.
  3. K. Arslan, R. Deszcz, R. Ezentas, M. Hotlos and C. Murathan, On generalized Robertson-Walker spacetimes satisfying some curvature condition, Turk. J. Math. 38, 353-373, 2014.
  4. A.L. Besse, Einstein Manifolds. Springer-Verlag, Berlin, 2008.
  5. Y.F. Cai, S. Capozziello, M.D. Laurentis and E.N. Sridakis, f(T) teleparallel gravity and cosmology, Rept. Prog. Phys. 79, 106901, 2016.
  6. R.R. Caldwell, A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state, Phys. Letter B 545, 23–29, 2002.
  7. S. Capozziello, C.A. Mantica and L.G. Molinari, Cosmological perfect uids in f(R)- gravity, Int. J. Geom. Methods Mod. Phys. 16, 1950008, 2019.
  8. S. Capozziello, C.A. Mantica and L.G. Molinari, Cosmological perfect fluids in higher- order gravity, Gen. Relativ. Gravit. 52, Article No: 36, 2020.
  9. S.M. Carroll, A. De Felice, V. Duvvuri, D.A. Easson, M. Trodden and M.S. Turner, The cosmology of generalized modified gravity models, Physics Rev. D 71, 063513, 2015.
  10. S. Chakraborty, An alternative f(R, T)-gravity theory and the dark energy problem, Gen. Relativ. Gravit. 45, 2039–2052, 2013.
  11. S.K. Chaubey, Y.J. Suh and U.C. De, Characterizations of the Lorentzian manifolds admitting a type of semi-symmetric metric connection, Anal.Math.Phys. 10, Article No: 61, 2020.
  12. U.C. De and Y.J. Suh, Some characterizations of Lorentzian manifolds, Int. J. Geom. Methods Mod. Phys. 16, 1950016, 2019.
  13. K.L. Duggal, Generalized Robertson-Walker spacetimes admitting evolving null hori- zons related to a Black Hole event horizon, Hindawi, International Scholarly Research Notices, 9312525, 2016.
  14. S. Dussault and V.A. Faraoni, A new symmetry of the spatially flat EinsteinFried- mann equations, Eur. Phys. J. C 80, Article No: 1002, 2020.
  15. A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata 7, 259–280, 1978.
  16. B.S. Guilfoyle and B.C. Nolan, Yang’s gravitational theory, Gen. Relativ. Gravitation 30 (3), 473–495, 1998.
  17. S. Güler and S. Altay Demirbağ, On Ricci symmetric generalized quasi Einstein space- times, Miskolc Math. Notes 16, 859-868, 2015.
  18. S. Güler and S. Altay Demirbağ, A study of generalized quasi Einstein spacetimes with applications in general relativity, Int. J. Theo. Phys. 55, 548-562, 2016.
  19. T. Harko, F.S.N. Lobo, S. Nojiri and S.D. Odintsov, f(R, T)-gravity, Phys. Rev. D 84, 024020, 2011.
  20. S.W. Hawking and G.F.R. Ellis, The Large-Scale Structure of Spacetimes, Cambridge University Press, Cambridge, 1973.
  21. D. Krupka, The trace decomposition problem, Beitrage Algebra Geom. 36, 303–315, 1995.
  22. S. Mallick and U.C. De, On Pseudo Q-symmetric spacetimes, Anal.Math.Phys. 9, 13331345, 2019.
  23. C.A. Mantica, Y.J. Suh, and U.C. De, A note on generalized Robertson-Walker space- times, Int. J. Geom. Meth. Mod. Phys. 13, 1650079, 2016.
  24. C.A. Mantica and L.G. Molinari, On the Weyl and the Ricci tensors of Generalized Robertson-Walker space-times, J. Math. Phys. 57 (10), 102502, 2016.
  25. C.A. Mantica, L.G. Molinari and U.C. De, A condition for a perfect fluid spacetime to be a generalized RobertsonWalker spacetime, J. Math. Phys. 57 (2), 022508, 2016, Erratum 57, 049901, 2016.
  26. C.A. Mantica and L.G. Molinari, Generalized RobertsonWalker spacetimes - A survey, Int. J. Geom. Methods Mod. Phys. 14 (3), 1730001, 2017.
  27. C.A. Mantica, L.G. Molinari, Y.J. Suh and S. Shenawy, Perfect-fluid, generalized Robertson-Walker spacetime, and Gray’s decomposition, J. Math. Phys. 60, 052506, 2019.
  28. S. Nojiri and S.D. Odintsov, Modified Gauss-Bonnet theory as gravitational alternative for dark energy, Phys. Lett. B 631 (1-2), 1-6, 2005.
  29. B. O’Neill, Semi-Riemannian Geometry With Applications to Relativity, New York: Academic Press, 1983.
  30. F. Özen Zengin, m-projectively flat spacetimes, Math. Reports, 14 (64), 363-378, 2012.
  31. E.M. Patterson, Some theorems on Ricci-recurrent spaces, J. Lond. Math. Soc. 27, 287–295, 1952.
  32. F. Rajabi and K. Nozari, Energy condition in unimodular f(R, T)-gravity, Eur. Phys. J. C 81, Article No: 247, 2021.
  33. R. Rani, B. Edgar and A. Barnes, Killing tensors and conformal Killing tensors from conformal Killing vectors, Class. Quantum Grav. 20 (11), 1929–1942, 2003.
  34. A. Restuccia and F. Tello-Ortiz, A new class of f(R)-gravity model with wormhole solutions and cosmological properties, Eur. Phys. J. C 80, Article No: 580, 2020.
  35. R. Sharma and A. Ghosh, Perfect fluid space-times whose energy-momentum tensor is conformal Killing, J. Math. Physics 51, 022504, 2010.
  36. L.C. Shepley and A.H. Taub, Spacetimes containing perfect fluids and having a van- ishing conformal divergence, Commun. Math. Phys. 5, 237–256, 1967.
  37. V. Singh and C.P. Singh, Modified f(R, T)-gravity theory and scalar field cosmology, Astrophys. Space Sci. 356, 153–162, 2015.
  38. N.S. Sinyukov, Geodesic mappings of Riemannian spaces, Nauka, Moscow (in Rus- sian), 1979.
  39. N.S. Sinyukov, Geodesic mappings of $L_2$ spaces, Izv. Vyssh. Ucheb. Zaved. Mat. 3, 57-61, (in Russian), 1982,
  40. T.P. Sotiriou and V. Faraoni, f(R) theories of gravity, Rev. Mod. Phys. 82, 451–497, 2010.
  41. H. Stephani, D. Kramer, M. MacCallum, C. Oenselaers and E. Herlt, Exact Solu- tions of Einstein’s Field Equations, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 2003.
  42. M. Walker and R. Penrose, On quadratic first integrals of the geodesic equations for {2, 2} spacetimes, Commun. Math. Phys. 18, 265274, 1970.
  43. M.X. Xu, T. Harko and S.D. Liang, Quantum cosmology of f(R, T)-gravity, Eur. Phys. J. C 76, Article No: 449, 2016.
  44. Y. Xu, G. Li and T. Harko, f(Q, T)-gravity, Eur. Phys. J. C 79, Article No: 708, 2019.
  45. J.Z. Yang, S. Shahidi and T. Harko, Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f(Q, T)-gravity, Eur. Phys. J. C 81, Article No: 111, 2021.