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

2021/12/28 by Puskar Mondal, Mondal, Puskar
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc

paper · pdf · doi:10.48550/arxiv.2112.14273

32 pages

arxiv created 2021/12/28 · openalex publication_date 2021/12/28 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeandersson2003elliptic, 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.

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