论文标题
时空正定理的平等情况
The case of equality for the spacetime positive mass theorem
论文作者
论文摘要
时空正理定理的刚度指出，可以将$（M，G，K）$带入质量状态的初始数据集$（M，G，K）$可以将质量消失的质量固定在Minkowski空间中。这是由Beig-Chruściel和Huang-Lee建立的，该假设是对能量和动量密度$μ$和$ J $的其他衰减假设。在本说明中，我们在维度3中给出了一个新的基本证明，该证明可以消除这些额外的衰减假设。我们的论点使用时空谐波函数和liouville的定理。我们还根据$（M，G，K）$的杀戮开发提供了替代证明。
The rigidity of the spacetime positive mass theorem states that an initial data set $(M,g,k)$ satisfying the dominant energy condition with vanishing mass can be isometrically embedded into Minkowski space. This has been established by Beig-Chruściel and Huang-Lee under additional decay assumptions for the energy and momentum densities $μ$ and $J$. In this note we give a new and elementary proof in dimension 3 which removes these additional decay assumptions. Our argument uses spacetime harmonic functions and Liouville's theorem. We also provide an alternative proof based on the Killing development of $(M,g,k)$.
