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arXiv · 1905.08968

Global regularity for Einstein-Klein-Gordon system with $U(1) \times \mathbb{R}$ isometry group, II

Haoyang Chen·Yi Zhou
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Abstract

This paper is devoted to the study of the global existence of smooth solutions for the 3+1 dimensional Einstein-Klein-Gordon systems with a $U(1) \times \mathbb{R}$ isometry group for a class of regular Cauchy data. In our first paper \cite{chen}, we reduce the Einstein equations to a 2+1 dimensional Einstein-wave-Klein-Gordon system. And we show that the first possible singularity can only occur at the axis. In this paper, we give a proof for the global regularity for the 2+1 dimensional system. Firstly, we show the non-concentration of the energy near the first possible singularity. Then, we prove that the global regularity holds for initial data with small energy.

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Haoyang Chen, Yi Zhou. 2019-05-22. Global regularity for Einstein-Klein-Gordon system with $U(1) \times \mathbb{R}$ isometry group, II. https://arxiv.org/abs/1905.08968

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