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Extrinsic Curvature and the Einstein Constraints

Harald P. Pfeiffer·James W. York
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Abstract

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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Harald P. Pfeiffer, James W. York. 2002-11-06. Extrinsic Curvature and the Einstein Constraints. https://doi.org/10.1103/physrevd.67.044022

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