Global exterior stability of the Minkowski space: coupled Einstein-Yang-Mills perturbations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911876836753408 |
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| author | Mondal, Puskar Yau, Shing-Tung |
| author_facet | Mondal, Puskar Yau, Shing-Tung |
| contents | Here we prove a global gauge-invariant radiation estimates for the perturbations of the $3+1$ dimensional Minkowski spacetime in the presence of Yang-Mills sources. In particular, we obtain a novel gauge invariant estimate for the Yang-Mills fields coupled to gravity in a double null framework in the Causal complement of a compact set of a Cauchy slice. A consequence of our result is the global exterior stability of the Minkowski space under coupled Yang-Mills perturbations. A special structure present both in the null Bianchi equations and the null Yang-Mills equations is utilized crucially to obtain the dispersive estimates necessary to conclude the global existence property. Direct use of Bel-Robinson and Yang-Mills stress-energy tensor to obtain the energy estimates is avoided in favor of weighted integration by parts taking advantage of the manifestly symmetric hyperbolic characteristics of null Bianchi and null Yang-Mills equations. Our result holds for any compact semi-simple gauge group. This is the first stability result of Minkowski space including a non-linear source. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03167 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global exterior stability of the Minkowski space: coupled Einstein-Yang-Mills perturbations Mondal, Puskar Yau, Shing-Tung General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Here we prove a global gauge-invariant radiation estimates for the perturbations of the $3+1$ dimensional Minkowski spacetime in the presence of Yang-Mills sources. In particular, we obtain a novel gauge invariant estimate for the Yang-Mills fields coupled to gravity in a double null framework in the Causal complement of a compact set of a Cauchy slice. A consequence of our result is the global exterior stability of the Minkowski space under coupled Yang-Mills perturbations. A special structure present both in the null Bianchi equations and the null Yang-Mills equations is utilized crucially to obtain the dispersive estimates necessary to conclude the global existence property. Direct use of Bel-Robinson and Yang-Mills stress-energy tensor to obtain the energy estimates is avoided in favor of weighted integration by parts taking advantage of the manifestly symmetric hyperbolic characteristics of null Bianchi and null Yang-Mills equations. Our result holds for any compact semi-simple gauge group. This is the first stability result of Minkowski space including a non-linear source. |
| title | Global exterior stability of the Minkowski space: coupled Einstein-Yang-Mills perturbations |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2211.03167 |