Neighbours of Einstein’s Equations: Connections and Curvatures
نویسنده
چکیده
Once the action for Einstein’s equations is rewritten as a functional of an SO(3, C) connection and a conformal factor of the metric, it admits a family of “neighbours” having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers. Email address: [email protected]
منابع مشابه
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Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein’s equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate subgroup of SL(3). We show how a set of ”neighbours” of Einstein’s equations arises because the subgroup may be chosen in different ways. An explicit example of a n...
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