论文标题
带电荷的准本地彭罗斯不平等现象
Quasi-local Penrose inequalities with electric charge
论文作者
论文摘要
Riemannian Penrose不平等是具有非负标量曲率的渐近平坦歧管的ADM质量与其最小表面的面积之间的显着几何不等性。也已经为爱因斯坦 - 马克斯韦尔方程式建立了Riemannian Penrose不平等的版本，其中质量上的下限也取决于电荷。在准本地质量的背景下，人们有兴趣确定是否以及对于哪些准局部质量定义，这些不平等的准本地版本也存在。 众所周知，Brown-York准局部质量满足了准局部Riemannian Penrose不平等，但是在Einstein-Maxwell方程式的背景下，人们期望一个准局部Riemannian Penrose不等式也应包括电荷的贡献。本文以Lu和Miao的思想以及名称为姓氏作者的思想为基础，以证明对具有边界的一类紧凑型歧管，证明了一些被带电的准局部penrose不平等现象。特别是，我们强加了在合适的Reissner-Nordström歧管中的边界对封闭表面的等距，该歧管是我们使用的准局部质量的参考歧管。在参考歧管质量为零和非零电荷的情况下，准局部质量的下限正好是由带电的Riemannian Penrose不平等给出的ADM质量的下限。
The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein-Maxwell equations, where the lower bound on the mass also depends on the electric charge. In the context of quasi-local mass, one is interested in determining if, and for which quasi-local mass definitions, a quasi-local version of these inequalities also holds. It is known that the Brown-York quasi-local mass satisfies a quasi-local Riemannian Penrose inequality, however in the context of the Einstein-Maxwell equations, one expects that a quasi-local Riemannian Penrose inequality should also include a contribution from the electric charge. This article builds on ideas of Lu and Miao and of the first-named author to prove some charged quasi-local Penrose inequalities for a class of compact manifolds with boundary. In particular, we impose that the boundary is isometric to a closed surface in a suitable Reissner-Nordström manifold, which serves as a reference manifold for the quasi-local mass that we work with. In the case where the reference manifold has zero mass and non-zero electric charge, the lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Riemannian Penrose inequality.
