论文标题
球形对称性中时空不等式的稳定性
Stability of the Spacetime Penrose Inequality in Spherical Symmetry
论文作者
论文摘要
我们制定并证明了与时空penrose不平等相关的稳定性声明，以$ n $二维的球形对称性，渐近平坦的初始数据满足了主要的能量条件。我们假设ADM质量接近最外面明显范围的一半面积半径，并且遵循广义的Jang方程方法，表明初始数据必须是由等距嵌入到接近Schwarzschild Spacetime外部区域的静态空间中的。也就是说，时间切片靠近Schwarzschild的时间切片，以保留固有的平坦距离，静态电势以$ l_ {loc}^2 $接近，并且初始数据外部曲率接近$ l^2 $中嵌入的第二个基本形式。
We formulate and prove the stability statement associated with the spacetime Penrose inequality for $n$-dimensional spherically symmetric, asymptotically flat initial data satisfying the dominant energy condition. We assume that the ADM mass is close to the half area radius of the outermost apparent horizon and, following the generalized Jang equation approach, show that the initial data must arise from an isometric embedding into a static spacetime close to to the exterior region of a Schwarzschild spacetime in the following sense. Namely, the time slice is close to the Schwarzschild time slice in the volume preserving intrinsic flat distance, the static potentials are close in $L_{loc}^2$, and the initial data extrinsic curvature is close to the second fundamental form of the embedding in $L^2$.
