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

TL;DR

This paper proves a semi-global existence and trapped surface formation in Einstein-Yang-Mills theory without symmetry assumptions, using a novel gauge-invariant approach to nonlinear estimates.

Contribution

It introduces a new gauge-invariant hierarchy of nonlinear estimates for Yang-Mills curvature in Einstein-Yang-Mills theory, enabling proof of trapped surface formation.

Findings

Semi-global existence from past null-infinity

Focusing of waves leads to trapped surface formation

Develops a novel gauge-invariant estimate hierarchy

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.