1998/05/08 by Mirta S. Iriondo, Mirta Iriondo, Carlos Kozameh +2
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #gr-qc
paper · pdf · doi:10.1063/1.533077
published as J.Math.Phys. 40 (1999) 2483-2493 · 28 pages, 7 figures
arxiv created 1998/05/08 · openalex publication_date 1999/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is shown that the main variable Z of the null surface formulation of GR is the generating family of a constrained Lagrange submanifold that lives on the energy surface H=0 and that its level surfaces Z=const yield Legendre submanifolds on that energy surface. Thus, the singularity structure of past null cones with apex at I+ is obtained by studying the projection map of the Legendre submanifolds to the configuration space. The behavior of the coordinate system defined by the variable Z at the caustic points is analyzed. It is shown that a single function Z(xa,ζ,ζ̄) cannot generate the conformal structure of an asymptotically flat space–time that satisfies the generic and weak energy condition.