Spacetimes with Pseudosymmetric Energy-momentum Tensor
Keywords:Perfect fluid, Einstein's field equation, pseudosymmetric energy-momentum tensor.
AbstractThe object of the present paper is to introduce spacetimes with pseudosymmetricenergy-momentum tensor. In this paper at first we consider the relation \(R(X,Y)\cdot T=fQ(g,T)\), that is, the energy-momentumtensor \(T\) of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetimeif the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetricand the converse is also true. Next we characterize the perfect fluid spacetimewith pseudosymmetric energy-momentum tensor. Finally, we consider conformally flat spacetime withpseudosymmetric energy-momentum tensor.
L. Amendola and S. Tsujikawa, Dark Energy: Theory and observations, Cambridge Univ. Press, Cambridge, 2010.
K. Arslan et al., On generalized Robertson-Walker spacetimes satisfying some curvature condition, Turk. J. Math., 38(2014), 353-373.
J. K. Beem and P. E. Ehrlich, Global Lorentzian Geometry, Marcel Dekker, New York, 1981.
O. Bertolami, Latest supernova data in the framework of generalized Chaplygin Gas Model, Mon. Not. R. Astron. Soc., 353(2004), p. 329.
E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian manifolds of conullity two, Singapore World Sci. Publishing, 1996.
M. C. Chaki and S. Roy, Spacetimes with covariant-constant energy-momentum tensor, Int. J. Theor. Phys., 35(1996), 1027-1032.
S. Chakraborty, N. Mazumder and R. Biswas, Cosmological Evolution Across Phantom Crossing and the Nature of the Horizon, Astrophys. Space Sci., 334(2011), 183-186.
B. Y. Chen and K. Yano, Hypersurfaces of a conformally
at spaces, Tensor(N.S.), 26(1972), 318-322.
C. J. S. Clarke, Singularities: Global and local aspects in Topological Properties and Global structure of spacetime, Edited by P. G. Bergmann and V. de Sabbata, Plenum Press, New York.
U. C. De and L. Velimirovic, Spacetimes with Semisymmetric energy momentum tensor, Int. J. Theor. Phys., 54(2015), 1779-1783.
B. P. Geroch, Spacetime structure from a global view point, Academic Press, New York, 1971.
S. Guler and S. A. Demirbag, A study of generalized quasi-Einstein spacetimes with applications in general relativity, Int. J. Theor. Phys., DOI-10.1007/s10773-015-2692 1.
S. W. Hawking and G. F. R. Ellis, The large-scale structure of spacetime, Cambridge Univ. Press, 1973.
P. S. Joshi, Global aspects in gravitation and cosmology, Oxford Science Publications, 1993.
O. Kowalski, An explicit classication of 3-dimensional Riemannian spaces satisfying R(X; Y ) R = 0; Czechoslovak Math. J., 46(121)(1996), 427-474
V. A. Mirzoyan, Ricci semisymmetric submanifolds(Russian), Itogi Nauki i Tekhniki. Ser.
Probl. Geom., 23, VINITI, Moscow, 1991, 29-66.
B. O'Neill, Semi-Riemannian Geometry, Academic Press, Inc. NY 1983.
H. Stephani, General Relativity-An Introduction to the Theory of Gravitational Field, Cambridge Univ. Press, Cambridge , 1982.
H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einstein's Field equations, Second Edition, Cambridge Monographs on Mathematical
Physics, Cambridge Univ. Press, Cambridge, 2003.
Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X; Y ) R = 0: I. The local version, J. Di. Geom. 17(1982), 531-582.
Z. I. Szabo, Classication and construction of complete hypersurfaces satisfying R(X; Y ) R = 0; Acta Sci. Math. (Szeged), 47(1981), 321-348.
Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X; Y ) R = 0: II. Global version, Geom. Dedicate, 19(1985), 65-108.
L. Verstraelen, Comments on pseudo-symmetry in the sense of Deszcz, Geometry and Topology of Submanifolds, 6(1994), 199-209, World Sci., Singapore.
A. Yildiz, U. C. De and A. Cetinkaya, On some classes of N(k)-quasi-Einstein manifolds, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 83(2013), 239-245.
F. O. Zengin, m-Projectively flat spacetimes, Math. Reports, 14(64)/4(2012), 363-370.
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