Null Cones from I+ and Legendre Submanifolds

MIRTA IRIONDO, CARLOS KOZAMEH Y TERESITA ROJAS

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 1999 vol. 40 p. 2483 - 2493

0022-2488

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,) cannot generate the conformal structure of an asymptotically flat space?time that satisfies the generic and weak energy condition.