Elliptic fibrations associated with the Einstein spacetimes

Details Elliptic fibrations associated with the Einstein spacetimes Elliptic fibrations associated with the Einstein spacetimes

1997-06-13

arxiv.org/abs/gr-qc/9706042v1

J.Math.Phys. 39 (1998) 5481-5490

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, Latex

Scientific paper

10.1063/1.532545

Given a conformally nonflat Einstein spacetime we define a fibration $P$ over it. The fibres of this fibration are elliptic curves (2-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the Weyl tensor of the Einstein metric. The fibration $P$ is a double branched cover of the bundle of null direction over the spacetime and is equipped with six linearly independent 1-forms which satisfy certain relatively simple system of equations.

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