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arxiv: gr-qc/0207095 · v2 · submitted 2002-07-24 · 🌀 gr-qc

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Extrinsic Curvature and the Einstein Constraints

Harald P. Pfeiffer , James W. York
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classification 🌀 gr-qc
keywords curvatureextrinsiceinsteinfunctionrepresentationweightbroughtcanonical
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The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors which involves a weight function. In stationary spacetimes, there is a natural choice of the weight function such that the transverse traceless part of the extrinsic curvature (or canonical momentum) vanishes.

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