A Study of Conformally Flat Quasi-Einstein Spacetimes with Applications in General Relativity
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Authors: V. H AND A. KUMARA H
DOI: 10.46793/KgJMat2103.477V
Abstract:
In this paper we consider conformally flat (QE)4 spacetime and obtained several important results. We study application of conformally flat (QE)4 spacetime in general relativity and Ricci soliton structure in a conformally flat (QE)4 perfect fluid spacetime.
Keywords:
Quasi-Einstein spacetime, perfect fluid spacetime, Einstein field equation, energy momentum tensor, Ricci solitons, conformal curvature tensor.
References:
[1] Z. Ahsan and S. A. Siddiqui, Concircular curvature tensor and fluid spacetimes, Internat. J. Theoret. Phys. 48 (2009), 3202–3212.
[2] L. Amendola and S. Tsujikawa, Dark Energy: Theory and Observations, Cambridge University Press, Cambridge, 2010.
[3] C. L. Bejan and M. Crasmareanu, Ricci solitons in manifolds with quasi-constant curvature, Publ. Math. Debrecen 78(1) (2011), 235–243.
[4] A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin, 1987.
[5] M. C. Chaki and S. Ray, Spacetimes with covariant constant energy momentum tensor, Internat. J. Theoret. Phys. 35(5) (1996), 1027–1032.
[6] M. C. Chaki and R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen 57 (2000), 297–306.
[7] B. Y. Chen and K. Yano, Hypersurfaces of a conformally flat space, Tensor (N.S.) 26 (1972), 315–321.
[8] A. De, C. Özgür and U. C. De, On conformally flat almost pseudo-Ricci symmetric spacetimes, Internat. J. Theoret. Phys. 51 (2012), 2878–2887.
[9] U. C. De and L. Velimirović, Spacetimes with semisymmetric energy momentum tensor, Internat. J. Theoret. Phys. 54 (2015), 1779–1783.
[10] G. F. R. Ellis, Relativistic Cosmology, in: R. K. Sachs (Ed.) General Relativity and Cosmology, Academic Press, London, 1971.
[11] S. Güler and S. A. Demirbağ, A study of generalized quasi Einstein spacetime with application in general relativity, International Journal of Theoretical Physics 55 (2016), 548–562.
[12] R. S. Hamilton, The Ricci flow on surfaces, Contemp. Math. 71 (1988), 237–261.
[13] S. Mallick and U. C. De, Spacetimes with pseudosymmetric energy momentum tensor, Communications Physics 26(2) (2016), 121–128.
[14] S. Mallick, Y. J. Suh and U. C. De, A spacetime with pseudo-projective curvature tensor, J. Math. Phys. 57 (2016), Paper ID 062501.
[15] D. G. Prakasha and B. S. Hadimani, η-Ricci soliton on para-Sasakian manifolds, J. Geom. 108 (2017), 383–392.
[16] S. Ray and Guha, On perfect fluid pseudo Ricci symmetric spacetime, Tensor (N.S.) 67 (2006), 101–107.
[17] A. A. Shaikh, D. W. Yoon and S. K. Hui, On quasi Eienstien spacetime, Tsuukiba J. Math. 33(2) (2009), 305–326.
[18] Venkatesha and D. M. Naik, Certain results on K-para conatct and para Sasakian manifold, J. Geom. 108 (2017), 939–952.
[19] Venkatesha and H. A. Kumara, Ricci soliton and geometrical structure in a perfect fluid spacetime with torse-forming vector field, Afr. Mat. (2019), DOI 10.1007/s13370-019-00679-y.
[20] K. Yano, Concircular geometry I, Proc. Imp. Acad. Tokyo. 16 (1940), 195–200.
[21] K. Yano, Integral Formulas in Riemannian Geometry, Marcel Dekker, New York, 1970.
[22] K. Yano and M. Kon, Structure on Manifold, Series in Pure Mathematics, World Scientific Publishing, Singapore, 1984.
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