论文标题
Bartnik质量最小化初始数据集和主要能量标量的改善性
Bartnik mass minimizing initial data sets and improvability of the dominant energy scalar
论文作者
论文摘要
我们介绍了主要能量标量的提高性概念，并引起了不加权性的强烈后果。特别是，我们证明，没有本地对称性的不可分解的初始数据集必须坐在携带全局杀死载体场的无局部完美流体时空内。我们还表明，从精确的意义上讲，主要的能量标量几乎可以改进。使用这些主要结果，我们提供了Bartnik质量最小化初始数据集的表征，这使Bartnik的固定猜想取得了长足的进步。 在途中，我们观察到，在大于八个的维度中，存在PP波反例（没有渐近平坦度的最佳衰减率）与时空正定理的平等情况。结果，在这些维度中，有反对巴特尼克的固定和严格阳性猜想的反示例。
We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik's stationary conjecture. Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, there exist counterexamples to Bartnik's stationary and strict positivity conjectures in those dimensions.
