空间维数至少四时时空Penrose不等式的带电约化
A Charged Reduction of the Spacetime Penrose Inequality in Spatial Dimensions at Least Four
OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。
具体内容
稿件在空间维数n≥4中研究单端带电初值数据的Penrose型不等式。作者借助配套的中性时空Penrose定理，在强衰减、未来陷阱、正面积等既定范围内，证明纯电性上面积不等式；数据可具任意内部拓扑与ADM动量，正负陷阱符号可逐边界选取。等号情形在m>|Q|及连通最外未来视界等假设下被分类为Reissner–Nordström–Tangherlini外部的整体类空切片，且仅限诱导磁二形式为零者。
- 在n≥4、带电主能量条件与div E=0下证明尖锐上面积不等式。
- 正面积与严格ADM类时性作为结论而非假设。
- m>|Q|时等号分类为Reissner–Nordström–Tangherlini外部切片。
AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。
英文原始摘要
Using the companion neutral spacetime Penrose theorem exactly at its stated strong-decay, future-trapped, positive-area, and future-timelike scope, we prove the sharp purely electric upper-area inequality in every spatial dimension n ≥ 4 for one-ended charged data satisfying the charged dominant energy condition and $`\mathop{\mathrm{div}}\nolimits _g E=0`$, with the specified decay, integrability, and finite-flux assumptions. The data may have arbitrary interior topology and ADM momentum, with a future or past trapping sign chosen independently on each boundary component. Positive enclosing area and strict ADM timelikeness are conclusions. The polynomial mass rearrangement is asserted only when the $`(n-2)`$nd power of the enclosing-area radius exceeds $`|Q|`$. When $`m\gt |Q|`$, equality under the stated connected, outermost, outer-area-minimizing future-horizon hypotheses recovers the original metric, second fundamental form, and electric field as a global spacelike slice of a Reissner–Nordström–Tangherlini exterior. The equality classification includes only slices whose induced magnetic two-form vanishes.
用户标记：未标记
固定编号：33ae7197e59ba5e8
原文来源