Asymptotic structure of the null surface formulation and the classical graviton

Abstract

The dynamical equations for the null surface formulation of general relativity for purely radiative spacetimes are derived. Those asymptotically flat spacetimes describe the nonlinear evolution of gravitational radiation and represent a classical graviton. The evolution equations constitute a set of three partial differential equations in a six-dimensional space and the source term is the free initial data of incoming gravitational radiation. The Huygens part of the wave propagation, backreaction terms, and source terms are identified in the resulting equations. An analysis of the range of validity of these equations based on the development of caustics is also given.