tailieunhanh - Spacetimes with pseudosymmetric energy-momentum tensor

The object of the present paper is to introduce spacetimes with pseudosymmetric energymomentum tensor. In this paper at first we consider the relation R(X,Y)· T = f Q(g,T), that is, the energy-momentum tensor T of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetime if the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetric and the converse is also true. | Communications in Physics, Vol. 26, No. 2 (2016), pp. 121-128 DOI: SPACETIMES WITH PSEUDOSYMMETRIC ENERGY-MOMENTUM TENSOR SAHANOUS MALLICK† Department of Mathematics, Chakdaha College, Chakdaha, Dist- Nadia, West Bengal, India UDAY CHAND DE Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India † E-mail: sahanousmallick@ Received 25 November 2015 Accepted for publication 09 June 2016 Abstract. The object of the present paper is to introduce spacetimes with pseudosymmetric energymomentum tensor. In this paper at first we consider the relation R(X,Y ) · T = f Q(g, T ), that is, the energy-momentum tensor T of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetime if the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetric and the converse is also true. Next we characterize the perfect fluid spacetime with pseudosymmetric energy-momentum tensor. Finally, we consider conformally flat spacetime with pseudosymmetric energy-momentum tensor. Keywords: perfect fluid spacetime, Einstein’s field equation, energy-momentum tensor, pseudosymmetric energy-momentum tensor. Classification numbers: [The Mathematics Subject Classification(2010)] 53B30, 53C50, 53C80. I. INTRODUCTION General relativity flows from the Einstein’s equation which implies that the energymomentum tensor is of vanishing divergence. This requirement of the energy-momentum tensor is satisfied if this tensor is covariant constant, that is, ∇T = 0, where ∇ denotes the operator of covariant differentiation with respect to the metric tensor g. In the general theory of relativity, energy-momentum tensor plays an important role and the condition on energy-momentum c 2016 Vietnam Academy of Science and Technology 122 SPACETIMES WITH PSEUDOSYMMETRIC ENERGY-MOMENTUM TENSOR tensor for a perfect fluid spacetime changes the nature of .