NONLINEAR WAVE EQUATIONS FOR RELATIVITY

TL;DR

This paper formulates gravitational radiation using nonlinear wave equations derived from Yang-Mills theory on curved spacetime, incorporating initial data constraints and evolution equations for the metric.

Contribution

It introduces a novel approach to describe gravitational radiation through nonlinear Yang-Mills wave equations on curved manifolds, including initial data and Lie-constraints.

Findings

Formulation of gravitational radiation via Yang-Mills wave equations

Inclusion of initial data problem with Lie-constraints

Evolution equations for the metric in tangent bundle

Abstract

Graviational radiation is described by canonical Yang-Mills wave equations on the curved space-time manifold, together with evolution equations for the metric in the tangent bundle. The initial data problem is described in Yang-Mills scalar and vector potentials, resulting in Lie-constraints in addition to the familiar Gauss-Codacci relations.