Null Surfaces and Legendre Submanifolds

Details Null Surfaces and Legendre Submanifolds Null Surfaces and Legendre Submanifolds

1998-05-08

arxiv.org/abs/gr-qc/9805027v1

J.Math.Phys. 40 (1999) 2483-2493

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, 7 figures

Scientific paper

10.1063/1.533077

It is shown that the main variable Z of the Null Surface Formulation of GR is the generating function of a constrained Lagrange submanifold that lives on the energy surface H=0 and that its level surfaces Z=const. are Legendre submanifolds on that energy surface. The behaviour of the variable Z at the caustic points is analysed and a genralization of this variable is discussed.

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