Construction of Initial Data Associated to the Characteristic Initial Value Problem for the Einstein-Yang-Mills-Higgs System

TL;DR

This paper develops a detailed method for constructing initial data on intersecting null hypersurfaces for the Einstein-Yang-Mills-Higgs system, extending previous techniques and setting the stage for future global existence results.

Contribution

It adapts Rendall's hierarchical method to the Einstein-Yang-Mills-Higgs system, providing detailed calculations for initial data construction on null hypersurfaces.

Findings

Successfully assigns initial data for the system

Provides detailed calculations for the data construction

Applicable to related Einstein field models

Abstract

We show how to assign initial data for the characteristic Einstein-Yang-Mills-Higgs system on two intersecting smooth null hypersurfaces. We successfully adapt the hierarchical method set up by A. D. Rendall to solve the same problem for the Einstein equations in vacuum and with perfect fluid source. Unlike the work of Rendall, many delicate calculations and expressions are given in details so as to address, in a forthcoming work, the issue of global resolution of the characteristic initial value problem for the Einstein-Yang-Mills-Higgs system. The method obviously applies to the Einstein-Maxwell and the Einstein-scalar field models.