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 radiativespacetimes are derived. Those asymptotically flat spacetimes describe the nonlinear evolution ofgravitational radiation and represent a classical graviton. The evolution equations constitute a set ofthree partial differential equations in a six-dimensional space and the source term is the free initial dataof incoming gravitational radiation. The Huygens part of the wave propagation, backreaction terms, andsource terms are identified in the resulting equations. An analysis of the range of validity of these equationsbased on the development of caustics is also given.