Space-time metrics inducing the radiation connection

Mathematics – Logic

Scientific paper

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Scientific paper

It is shown that Lorentzian manifolds giving rise to the radiation connection, i.e. such that the canonical connection induces a unique connection on an isotropic hypersurface, are of type D or conformally flat in Petrov classification, generalizing the Robinson-Bertotti electromagnetic universe with cosmological constant. Under an holonomy hypothesis it is deduced that the underlying space-time manifold is a direct product of two two-dimensional spaces, one of them being space-like, and the other one time-like.

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