Lightlike Hypersurfaces and General Relativity
Here we investigate some possible choices (Ricci flat, Einstein and pure radiation type) of the induced energy momentum tensor on a class of totally geodesic lightlike hypersurfaces M of 4-dimensional spacetime manifolds. We show that there does not exist any induced non-singular electromagnetic energy momentum tensor field and its singular type belongs to a class of pure radiation fields. Based on this, in sections 9.2 and 9.3, we study some properties of induced conformal and affine conformal vector fields, on M, respectively. Finally, we present a few examples of lightlike hypersurfaces of physically significant spacetimes of relativity.
KeywordsVector Field Energy Momentum Tensor Spacelike Hypersurface Constant Scalar Curvature Einstein Field Equation
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