Fwd: Relation between Connection and Tetrad



Subject: Relation between Connection and Tetrad
Date: Wed, 25 Mar 2009 07:20:24 EDT

This is given by the tetrad postulate, and replaces the incorrect relation between the connection and metric of the obsolete gravitational physics. The tetrad is a more fundamental building block of geometry than the metric, and the tetrad was first described as the vielbein (many legged), or in four dimensions the vierbein (four legged). The incorrect symmetric connection of the old physics was related to the symmetric metric by use of three applications of metric compatibility in cyclic permutation (see Carroll chapter 3 or GCUFT 1 to 5). The tetrad postulate does not rely on metric compatibility at all, so is more fundamental. The usual symmetric metric is a product of tetrads. However there can be a more general product of tetrads, giving a more general metric (see early ECE papers or GCUFT1).

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