Global existence of the solution to Einstein-Yang-Mills-Higgs equations with small initial datum

TL;DR

This paper proves that the Einstein-Yang-Mills-Higgs equations have globally existing solutions when starting from sufficiently small initial data, using wave coordinates and Lorentzian gauge conditions.

Contribution

It establishes the first known global existence result for the EYMH system with small initial data, filling a gap in the mathematical understanding of these equations.

Findings

Global solutions exist for small initial data

Method relies on wave coordinates and Lorentzian gauge

No prior similar results in EYMH equations

Abstract

The problem involved in this paper is the global existence of the solution to the $\mathfrak{su}(2)$-Einstein-Yang-Mills-Higgs(EYMH) equation. The approach we employ stems from H. Lindblad and I. Rodnianski and is dependent of wave coordinates and Lorentzian gauge conditions. Our main conclusion is that the EYMH system admits global existence provided the initial datum are sufficiently small. To the best of our knowledge, there is no similar result in the area of EYMH equations.