Gravitation Singularities of the Caustic Type

Details Gravitation Singularities of the Caustic Type Gravitation Singularities of the Caustic Type

1994-04-13

arxiv.org/abs/gr-qc/9404024v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX Preprint MSU-TP-94-31

Scientific paper

In view of the well-known correspondence between gravitational fields and space-time distributions on a world manifold X, the criterion of gravitation singularities as singularities of these distributions is suggested. In the germ terms, singularities of a (3+1) distribution look locally like singularities of a foliation whose leaves are level surfaces of a real function f on X. If f is a single-valued function, changes of leave topology at critical points of f take place. In case of a multi-valued function f, one can lift the foliation to the total space of the cotangent bundle over X, then extend it over branch points of f and project this extension onto X. Singular points of this projection constitute a Lagrange map caustic by Arnol'd.

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