Provides a first detailed proof that (1+3)-dimensional Minkowski spacetime is stable in the exterior region under the fully coupled, fully nonlinear Einstein-Yang-Mills equations in the Lorenz gauge, with Yang-Mills fields valued in the Lie algebra of an arbitrary compact Lie group and no assumption of spherical symmetry. Starting from sufficiently small initial data in a suitable energy norm, it establishes well-posedness of the exterior Cauchy development and convergence, in the Lorenz gauge and wave coordinates, to the zero Yang-Mills field and flat Minkowski space. The proof adapts the null-frame decomposition of Lindblad and Rodnianski to a hyperbolic system that fails the null condition, and highlights that in the non-abelian case stability is an intrinsically gauge-dependent statement because gauge transformations change the very PDEs satisfied by the Yang-Mills potential.
We study the Einstein-Yang-Mills system in both the Lorenz and harmonic gauges, where the Yang-Mills fields are valued in any arbitrary Lie algebra $\cal G$, associated to any compact Lie group $G$. …