球对称Liu-Yau质量的局部化Penrose不等式
Localized Penrose inequality for the Liu-Yau mass in spherical symmetry
摘要：
对于一个渐近平坦的初始数据，彭罗斯不等式给出了时空的Arnowitt-Deser-Misner总质量的一个下界，这个下界是用代表黑洞的某些表面的面积来表示的。这是对著名的正质量定理的深刻而优美的改进，在引力坍缩的研究中起着重要的作用。如果有足够的质量集中在一个有限的区域内，也会发生引力坍缩。这促使我们寻求彭罗斯不等式的本地化版本。在这封信中，我们成功地对球对称的刘丘准定域质量的这种形式作了精确的陈述。
英文摘要：
For an asymptotically flat initial data, the Penrose inequality gives a lower bound of the Arnowitt-Deser-Misner total mass of a spacetime in terms of the area of certain surfaces representing black holes. This is a deep and beautiful refinement of the famous positive mass theorem and it plays an important role in the study of gravitational collapse. Gravitational collapse can also happen if sufficient mass is concentrated into a finite region. This motivates us to seek a localized version of the Penrose inequality. In this Letter, we successfully make a precise statement of this form for the Liu-Yau quasi-local mass in spherical symmetry.
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