Author(s): FZ Chagpar, GP Pokhariyal and SK Moindi

Abstract: The P₁ - curvature tensor defined from W₃ - curvature tensor has been studied in the space time of general relativity. The Bianchi like differential identity is satisfied by P₁ - tensor if and only if the Ricci tensor is of Codazzi type. It is shown that Einstein like field equations can be expressed with the help of the contracted part of P₁ - tensor, which is conserved if the energy momentum tensor is Codazzi type. Considering P₁ -flat space time satisfying Einstein’s field equations with cosmological term, the existence of Killing vector field ξ is shown if and only if the Lie derivative of the energy-momentum tensor vanishes with respect to ξ, as well as admitting a conformal Killing vector field is established if and only if the energy-momentum tensor has the symmetry inheritance property. Finally for a P₁ - flat perfect fluid space time satisfying Einstein’s equations with cosmological term, some results are obtained.

DOI: 10.22271/maths.2021.v6.i1b.645

Pages: 148-152 | Views: 1024 | Downloads: 20

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