带电荷的时空Penrose不等式与原始数据刚性
The spacetime Penrose inequality with charge and original-data rigidity
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具体内容
稿件研究带电荷的三维单端初始数据的尖锐时空Penrose上面积不等式。作者声称在所述能量、衰减与陷阱假设下，允许任意第二基本形式、非零ADM动量与非连通边界；以m为不变ADM质量、Q为总荷大小、r_A为最小包围面积半径，得到m≥Q与r_A≤m+√(m²-Q²)，多项式质量界仅在r_A>Q时断言。摘要表示当m>Q且满足连通、最外、外面积最小化未来视界假设时，等号把原始数据识别为双荷Reissner–Nordström的光滑类空切片。
- 对三维单端带电源无初始数据证明尖锐上面积不等式
- 得到m≥Q与r_A≤m+√(m²-Q²)，多项式质量界仅在r_A>Q时断言
- 等号在所述视界假设下识别为双荷Reissner–Nordström的光滑类空切片
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英文原始摘要
Under the stated energy, decay, and trapping hypotheses, we prove the sharp charged spacetime Penrose upper-area inequality for one-ended three-dimensional initial data with source-free electric and magnetic fields. The theorem allows arbitrary second fundamental form, nonzero ADM momentum, and disconnected boundary. Writing m for invariant ADM mass, Q for total charge magnitude, and rA for the minimum-enclosing-area radius, the bound is m ≥ Q and $`r_A\le m+\sqrt{m^2-Q^2}`$. The polynomial mass bound $`m\ge(r_A+Q^2/r_A)/2`$ is asserted only when $`r_A\gt Q`$. When m > Q, equality under the stated connected, outermost, outer-area-minimizing future-horizon hypotheses identifies the original data as a smooth spacelike slice of dyonic Reissner–Nordström, including smooth attachment at the future horizon.
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