98-207 Sen, D. K.

Relativity on 3-manifolds (25K, TeX) Mar 18, 98

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Abstract. We present a new formulation of General Relativity in an entirely 3-dimensional pseudo--Riemannian space. Here the basic idea is to represent local physical observers by nonsingular 3-dimensional vector fields of bounded length and the dynamics of physical fields by the flows of vector fields. The flow parameter plays the role of local time for each physical observer, and the Lie derivative replaces the time derivative. Some wellknown solutions and a new solution of the vacuum Einstein field equations are formulated in this framework.

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