Inequivalent metrics with equal spin coefficients
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The spin coefficients, the curvature tensor, and the first covariant derivative of the curvature tensor are shown to be insufficient for a complete description of a gravitational field. The inadequacy of the description becomes evident when a set of (unphysical) inequivalent metrics is constructed which cannot be distinguished by only examining these entities. The inequivalence manifests itself in the second covariant derivative.
KeywordsDifferential Geometry Covariant Derivative Gravitational Field Curvature Tensor Spin Coefficient
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