Local well-posedness of the Einstein-Yang-Mills system in CMCSHGC gauge

Abstract

We study the local well-posedness of the Einstein-Yang-Mills equations in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge (CMCSHGC). In this choice of gauge, the complete Einstein-Yang-Mills equations reduce to a coupled elliptic-hyperbolic system. Utilizing the method developed by Andersson and Moncrief \cite{andersson2003elliptic}, we establish the existence of a unique, local, continuous-in-time solution of this coupled system. This yields an `in time' continuation criteria of the solutions which is to be used in the potential future proof of an improved continuation criteria for this coupled system utilizing Moncrief's light cone estimate technique.

32 pages