Abstract
Given a conformally nonflat Einstein space–time we define a fibration P̃ over it. The fibers of this fibration are elliptic curves (two-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the Weyl tensor of the Einstein metric. The fibration P̃ is a double branched cover of the bundle 𝒫 of null direction over the space–time and is equipped with six linearly independent one-forms which satisfy a certain relatively simple system of equations.
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