Classical Solutions of Higher Dimensional Einstein-Maxwell-Higgs System With Nontrivial Potential: Global Existence and Completeness

Abstract

We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs system in the framework of Bondi coordinates. As a first step, the problem is reduced to a single first-order integro-differential equation by defining a generalized ansatz function. Then, we employ contraction mapping to show that there exists the unique fixed point of the problem. For a given small initial data, we prove the existence of a global classical solution. Finally, by introducing local mass and local charge functions in higher dimensions, we also show the completeness property of the spacetimes.

45 pages, no figure. arXiv admin note: text overlap with arXiv:2304.09449