Research Article
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Year 2022, Volume: 51 Issue: 1, 101 - 112, 14.02.2022

Sinem Güler , U.c. De

https://doi.org/10.15672/hujms.927654
Cited By: 2

Abstract

References

  • [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.

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

Year 2022, Volume: 51 Issue: 1, 101 - 112, 14.02.2022

Sinem Güler , U.c. De

https://doi.org/10.15672/hujms.927654
Cited By: 2

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.

Keywords

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

References

  • [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.
There are 45 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sinem Güler 0000-0001-9994-2927

U.c. De 0000-0002-8990-4609

Publication Date February 14, 2022
Published in Issue Year 2022 Volume: 51 Issue: 1

Cite

APA Güler, S., & De, U. (2022). Perfect fluid spacetimes, Gray’s decomposition and $f(\mathcal{R}, {T})$-gravity. Hacettepe Journal of Mathematics and Statistics, 51(1), 101-112. https://doi.org/10.15672/hujms.927654
AMA Güler S, De U. Perfect fluid spacetimes, Gray’s decomposition and $f(\mathcal{R}, {T})$-gravity. Hacettepe Journal of Mathematics and Statistics. February 2022;51(1):101-112. doi:10.15672/hujms.927654
Chicago Güler, Sinem, and U.c. De. “Perfect Fluid Spacetimes, Gray’s Decomposition and $f(\mathcal{R}, {T})$-Gravity”. Hacettepe Journal of Mathematics and Statistics 51, no. 1 (February 2022): 101-12. https://doi.org/10.15672/hujms.927654.
EndNote Güler S, De U (February 1, 2022) Perfect fluid spacetimes, Gray’s decomposition and $f(\mathcal{R}, {T})$-gravity. Hacettepe Journal of Mathematics and Statistics 51 1 101–112.
IEEE S. Güler and U. De, “Perfect fluid spacetimes, Gray’s decomposition and $f(\mathcal{R}, {T})$-gravity”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, pp. 101–112, 2022, doi: 10.15672/hujms.927654.
ISNAD Güler, Sinem - De, U.c. “Perfect Fluid Spacetimes, Gray’s Decomposition and $f(\mathcal{R}, {T})$-Gravity”. Hacettepe Journal of Mathematics and Statistics 51/1 (February 2022), 101-112. https://doi.org/10.15672/hujms.927654.
JAMA Güler S, De U. Perfect fluid spacetimes, Gray’s decomposition and $f(\mathcal{R}, {T})$-gravity. Hacettepe Journal of Mathematics and Statistics. 2022;51:101–112.
MLA Güler, Sinem and U.c. De. “Perfect Fluid Spacetimes, Gray’s Decomposition and $f(\mathcal{R}, {T})$-Gravity”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, 2022, pp. 101-12, doi:10.15672/hujms.927654.
Vancouver Güler S, De U. Perfect fluid spacetimes, Gray’s decomposition and $f(\mathcal{R}, {T})$-gravity. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):101-12.

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https://dergipark.org.tr/en/pub/hujms