Asymptotic behaviour of the Einstein-Yang-Mills-Higgs system in a Bianchi type I model

10.5556/j.tkjm.55.2024.5127

Nguelemo Kenfack Abel；Djiofack Francis Etienne；Dongo David；Remy Magloire Etoua

Einstein equations ； Yang-Mills field ； Higgs field ； Bianchi type I model ； global solution ； asymptotic behaviour

Tamkang Journal of Mathematics

55卷3期（2024 / 09 / 01）

223 - 239

英文

We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour.