时空Penrose不等式：包围面积、电荷与刚性
Spacetime Penrose inequalities: enclosing area, charge, and rigidity
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具体内容
稿件研究三维与四维空间中不变ADM质量与最小包围面积之间的尖锐时空Penrose不等式。作者声称在各自指定端约定下，中性数值结果允许任意第二基本形式、非零动量、非连通弱未来陷阱边界及有限多个端。摘要表示在所述视界假设下，中性不等式取等可把原始外部数据重构为三维Schwarzschild时空与四维Schwarzschild–Tangherlini时空的类空切片；四维等号定理针对连通单端外部。另证三维电磁荷上面积不等式及局部Schwarzschild–反de Sitter不等式。
- 证明三维与四维不变ADM质量与最小包围面积的尖锐时空Penrose不等式
- 中性不等式取等时重构Schwarzschild及Schwarzschild–Tangherlini切片
- 另证三维电磁荷上面积不等式与局部Schwarzschild–反de Sitter不等式
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英文原始摘要
We prove sharp spacetime Penrose inequalities for invariant ADM mass and minimum enclosing area in three and four spatial dimensions. Under their respective designated-end conventions, the neutral numerical results allow arbitrary second fundamental form, nonzero momentum, disconnected weakly future trapped boundary, and finitely many ends. Under the stated horizon hypotheses, equality for the neutral inequalities reconstructs the original exterior data as spacelike slices of Schwarzschild spacetime in three dimensions and Schwarzschild–Tangherlini spacetime in four; the four-dimensional equality theorem concerns a connected, one-ended exterior. We also prove a three-dimensional electric–magnetic charged upper-area inequality for one-ended data with nonzero momentum, with separate purely electric rest-frame corollaries allowing finitely many ends. Finally, for each fixed transverse-traceless seed and prescribed decaying solution branch, we prove a local Schwarzschild–anti-de Sitter inequality.
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