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arXiv · 2302.06915

Formation of trapped surfaces in the Einstein-Yang-Mills system

Nikolaos Athanasiou·Puskar Mondal·Shing-Tung Yau
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Abstract

We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions. More precisely, we prove a scale-invariant semi-global existence theorem from past null-infinity and show that the focusing of the gravitational and/or chromoelectric-chromomagnetic waves could lead to the formation of a trapped surface. Adopting the signature for decay rates approach introduced in \cite{A19}, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yields the desired semi-global existence result. Once semi-global existence has been established, the formation of a trapped surface follows from a standard ODE argument.

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Nikolaos Athanasiou, Puskar Mondal, Shing-Tung Yau. 2023-02-14. Formation of trapped surfaces in the Einstein-Yang-Mills system. https://arxiv.org/abs/2302.06915

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