Future stability of the 1+3 Milne model for the Einstein-Klein-Gordon system
Future stability of the 1+3 Milne model for the Einstein-Klein-Gordon system
复制标题
爱因斯坦-克莱因-戈登系统 1 3 Milne 模型的未来稳定性
DOI：
10.1088/1361-6382/ab4dd3
复制
发表时间：
2019
影响因子：
3.5
通讯作者：
Wang Jinhua
中科院分区：
文献类型：
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作者：
Wang Jinhua
研究了爱因斯坦-克莱因-戈登(EKG)系统1+3维Milne模型的小扰动。我们证明了非线性未来稳定性，并证明了扰动时空是未来因果大地完备的。作为证明，我们在常平均曲率(CMC)规范下工作，并集中于Bianci-Klein-Gordon方程的1+3分裂。此外，我们将Bianci-Klein-Gordon方程视为发展方程，建立了能量格式，即我们只交换具有空间协变导数的Bianci-Klein-Gordon方程，而不允许法向导数。我们提出了一些关于失误的精细化估计和能量估计的层次，以结束能量争论。
We study the small perturbations of the 1+ 3-dimensional Milne model for the Einstein–Klein–Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete. For the proof, we work within the constant mean curvature (CMC) gauge and focus on the 1+ 3 splitting of the Bianchi–Klein–Gordon equations. Moreover, we treat the Bianchi–Klein–Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi–Klein–Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.