Null Surfaces and the Bach Equations

MIRTA IRIONDO, CARLOS KOZAMEH Y TERESITA ROJAS

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 1997 vol. 38 p. 4714 - 4729

0022-2488

It is shown that the integrability conditions that arise in the Null Surface Formulation (NSF) of general relativity (GR) impose a field equation on the local null surfaces which is equivalent to the vanishing of the Bach tensor. This field equation is written explicitly to second order in a perturbation expansion. The field equation is further simplified if asymptotic flatness is imposed on the underlying space-time. The resulting equation determines the global null surfaces of asymptotically flat, radiative space-times. It is also shown that the source term of this equation is constructed from the free Bondi data at I. Possible generalizations of this field equation are analyzed. In particular we include other field equations for surfaces that have already appeared in the literature which coincide with ours at a linear level. We find that the other equations do not yield null surfaces for GR.