P1-Curvature tensor in the space time of general relativity

FZ Chagpar, Pokhariyal GP, Moindi SK. "P1-Curvature tensor in the space time of general relativity." International Journal of Statistics and Applied Mathematics. 2021;6(1):148-152.


The P1 - curvature tensor defined from W3 - curvature tensor has been studied in the spacetime 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 spacetime satisfying Einstein’s equations with cosmological term, some results are obtained


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