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

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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.

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Acknowledgements

Both authors are grateful to Prof. Naqing Xie for fruitful discussions. The first author especially thanks him for his kind guidance. The authors also thank the referees for their helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Haoyang Chen

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Yi Zhou

Authors
  1. Haoyang Chen
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  2. Yi Zhou
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Corresponding authors

Correspondence to Haoyang Chen or Yi Zhou.

Additional information

This work was supported by the Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), the Ministry of Education of China, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, the National Natural Science Foundation of China (Nos. 11421061, 11726611, 11726612), 973 Program (No. 2013CB834100) and 111 Project.

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Chen, H., Zhou, Y. Global Regularity for Einstein-Klein-Gordon System with U(1) × R Isometry Group, I. Chin. Ann. Math. Ser. B 41, 939–966 (2020). https://doi.org/10.1007/s11401-020-0240-7

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  • DOI: https://doi.org/10.1007/s11401-020-0240-7

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