Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.
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Explicit construction of the Plebanski matter source T^i via Kulkarni-Nomizu lifting of the trace-free energy-momentum tensor that reproduces Krasnov's definition and yields the Reissner-Nordström-de Sitter solution.
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Warped Product Einstein Manifolds in Four Dimensions
Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.
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On the Plebanski Formulation with Energy Momentum
Explicit construction of the Plebanski matter source T^i via Kulkarni-Nomizu lifting of the trace-free energy-momentum tensor that reproduces Krasnov's definition and yields the Reissner-Nordström-de Sitter solution.
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