Dyadic Analysis of Space-Time Congruences

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Abstract
A physical 3-vector and dyadic formalism for the treatment of general relativistic problems is derived, by systematic introduction of a proper tetrad field. The method is especially appropriate when there exists a physically or geometrically preferred timelike congruence; all quantities in the formalism are then shown to have immediate physical interpretation as proper local observables. A complete and nonredundant set of equations for the analysis of timelike congruences is developed in this operational language. Application is made to some simple examples involving local observations, and the direct measurement of the Riemann tensor discussed.

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