有源的线性化爱因斯坦方程

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-07-08 DOI:10.1007/s11005-024-01841-9

Peter Hintz

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引用次数: 0

摘要

在一般维度的真空时空中，我们研究了线性化爱因斯坦真空方程与空间紧凑支撑且（必然）无发散源。我们证明，以时空上的基林矢量场定义的源的适当电荷的消失是空间紧凑支撑的度量扰动类中可解性的必要条件和充分条件。这一证明结合了蒙克里夫的经典结果以及科维诺-肖恩（Corvino-Schoen）和克鲁希尔-德雷（Chruściel-Delay）提出的具有支撑控制的线性化约束方程的可解性理论。

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The linearized Einstein equations with sources

On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source, defined in terms of Killing vector fields on the spacetime, is necessary and sufficient for solvability within the class of spatially compactly supported metric perturbations. The proof combines classical results by Moncrief with the solvability theory of the linearized constraint equations with control on supports developed by Corvino–Schoen and Chruściel–Delay.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.