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

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.