关于渐近平直史瓦西光锥中常时空平均曲率曲面的唯一性
On the uniqueness of surfaces of constant spacetime mean curvature in asymptotically Schwarzschildean lightcones
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中文总结 AI 辅助
研究渐近平直史瓦西光锥中常时空平均曲率曲面的唯一性，证明对于一般渐近平直概念存在唯一渐近平直叶状结构，此前已证存在性，此次在更弱假设下证唯一性。
中文摘要 AI 辅助
本文研究质量\(m>0\)的渐近平直史瓦西光锥中常时空平均曲率曲面的唯一性。对于相当一般的渐近平直概念，证明了存在由常时空平均曲率曲面构成的唯一渐近平直叶状结构。该叶状结构具有邦迪能量\(m\)且邦迪线性动量为零。作者此前已证明此类叶状结构的存在性，但仅在非常受限的曲面类中证明了唯一性。尽管该受限曲面类对构造是必要的，但本文表明在弱得多的假设下叶状结构事后是唯一的。
英文摘要
In this paper, we address the uniqueness of surfaces of constant spacetime mean curvature in an asymptotically Schwarzschildean lightcone of mass $m>0$. We prove that there exists a unique asymptotically flat foliation by surfaces of constant spacetime mean curvature for a fairly generic notion of asymptotic flatness. This foliation has Bondi energy $m$ and vanishing Bondi linear momentum. The authors have already established the existence of such a foliation in previous work, but proven uniqueness only in a very restrictive class of surfaces. Although this restrictive class of surfaces was necessary for the construction, here we show that the foliation is a posteriori unique under significantly weaker assumptions.
