Area bound for surfaces in generic gravitational field
Area bound for surfaces in generic gravitational field
复制标题
一般引力场中表面的区域边界
DOI：
10.1093/ptep/ptab089
复制
发表时间：
2021
影响因子：
3.5
通讯作者：
Hirotaka Yoshino
中科院分区：
文献类型：
--
作者：
Keisuke Izumi;Yoshimune Tomikawa;Tetsuya Shiromizu;Hirotaka Yoshino
我们将吸引重力探测曲面定义为具有正平均曲率的紧致2曲面（对于常数），满足局部逆平均曲率流，其中是向外单位法线方向的导数。对于渐近平坦空间，证明了任意AGPS满足面积不等式，其中为其面积，为Arnowitt-Deser-Misner质量。当空间与史瓦西时空的常数超曲面等距且是一个具有的曲面时，实现等式。我们采用了逆平均曲率流动和保形流动两种方法。因此，我们的结果适用于具有多个组件的情况。对于反德西特（AdS）空间，导出了一个类似的不等式，但只能通过使用逆平均曲率流来证明。我们还讨论了具有渐近局部ad空间的情况。
We define an attractive gravity probe surface (AGPS) as a compact 2-surfacewith positive mean curvaturesatisfying(for a constant) in the local inverse mean curvature flow, whereis the derivative ofin the outward unit normal direction. For asymptotically flat spaces, any AGPS is proved to satisfy the areal inequality, whereis the area ofandis the Arnowitt–Deser–Misner mass. Equality is realized when the space is isometric to theconstant hypersurface of the Schwarzschild spacetime andis ansurface with. We adapt the two methods of the inverse mean curvature flow and the conformal flow. Therefore, our result is applicable to the case wherehas multiple components. For anti-de Sitter (AdS) spaces, a similar inequality is derived, but the proof is performed only by using the inverse mean curvature flow. We also discuss the cases with asymptotically locally AdS spaces.