Global Regularity for Einstein-Klein-Gordon System with U(1) × R Isometry Group, I

Abstract

This is the first of the two papers devoted to the study of global regularity of the 3 + 1 dimensional Einstein-Klein-Gordon system with a U(1) × ℝ isometry group. In this first part, the authors reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2 + 1 dimensional system. Then, the authors will give energy estimates and construct the null coordinate system, under which the authors finally show that the first possible singularity can only occur at the axis.

Keywords

Einstein-Klein Gordon system / Cauchy problem / Energy estimates / Null coordinate / First singularity