On the global well-posedness of the Einstein-Yang-Mills system. (English) Zbl 1516.83004
Summary: In this paper, we present a partial result on the global well-posedness of the Cauchy problem for the Einstein-Yang-Mills system in constant mean extrinsic curvature spatial harmonic and generalized Coulomb gauges as introduced in the work of P. Mondal [“Local well-posedness of the Einstein-Yang-Mills system in CMCSHGC gauge”, Preprint, arXiv:2112.14273]. We give a small-data global existence theorem for a family of \(n + 1\) dimensional spacetimes with \(n \geq 4\), utilizing energy arguments presented in the work of L. Andersson and V. Moncrief [J. Differ. Geom. 89, No. 1, 1–47 (2011; Zbl 1256.53035)]. We observe that these energy arguments will fail for \(n = 3\) due to the conformal invariance of \(3 + 1\) Yang-Mills equations and present a gauge-covariant formulation of the Einstein-Yang-Mills system in \(3 + 1\) dimensions to show that an energy argument cannot be used to prove the global well-posedness result, regardless of the choice of gauge.
©2023 American Institute of Physics
©2023 American Institute of Physics
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 53Z05 | Applications of differential geometry to physics |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 83F05 | Relativistic cosmology |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
Citations:
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