2-凸初值集的带电荷Penrose不等式
The Penrose inequality with charge for 2-convex initial data sets
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中文总结 AI 辅助
本研究在2-凸性条件下证明了带电荷Penrose不等式，基于Dong的不带电情形证明框架，修改单调性公式纳入电荷项，得到ADM质量与视界面积、总电荷的关系及等号成立条件。
中文摘要 AI 辅助
我们在Dong最近提出的2-凸性条件下证明了带电荷的Penrose不等式。更确切地说，给定一个完备、连通且渐近平直的Einstein-Maxwell初值集$(M,g,k; E,B)$，它满足带电荷的主能量条件和2-凸性条件，拥有无散的电磁矢量场$(E,B)$以及一个连通的最外层过去表观视界$Σ$，且该视界满足$|Σ| \u003e 4πq^2$（其中$q$为总电荷），我们证明ADM质量$m$满足如下不等式：$m\geq \sqrt{\frac{|Σ|}{16π}} + q^2 \sqrt{\fracπ{|Σ|}}$，等号成立当且仅当$k \equiv 0$且$(M,g;E,B)$与亚极端Reissner-Nordström时空的标准切片等距。基于Dong对不带电荷情形的证明，我们使用了他的$\u003cstrong\u003eP\u003c/strong\u003e$-逆平均曲率流及其弱表述，该表述仅依赖于$(g,\u003cstrong\u003eP\u003c/strong\u003e)$，因此可直接应用于带电荷情形。我们工作的创新点在于修改了单调性公式，以纳入额外的电荷项。对于时间对称数据（$k \equiv 0$），该流退化为经典的逆平均曲率流，我们的单调性公式退化为带电荷Hawking质量的Jang单调性，从而恢复了带电荷的Riemannian Penrose不等式。
英文摘要
We prove the Penrose inequality with charge under the 2-convexity condition recently introduced by Dong. More precisely, given a complete, connected and asymptotically flat Einstein-Maxwell initial data set $(M,g,k; E,B)$ satisfying the charged dominant energy and the 2-convexity conditions, with divergence-free electromagnetic vector fields $(E,B)$ and a connected outermost past apparent horizon $Σ$ that satisfies $|Σ| \geq 4πq^2$ - where $q$ is the total charge - we show that the following inequality for the ADM mass $m$ holds: $m\geq \sqrt{\frac{|Σ|}{16π}} + q^2 \sqrt{\fracπ{|Σ|}}$, with equality if and only if $k \equiv 0$ and $(M,g;E,B)$ is isometric to a canonical slice of sub-extremal Reissner-Nordström spacetime. Building on Dong's proof of the uncharged case, we use his $\mathbf{P}$-inverse mean curvature flow and its weak formulation, which only depends on $(g,\mathbf{P})$ and hence applies to the charged setting unchanged. The novelty of our work is the modification of the monotonicity formula to account for the additional charge term. For time-symmetric data ($k \equiv 0$), the flow reduces to the classical inverse mean curvature flow and our monotonicity formula to Jang's monotonicity of the charged Hawking mass, recovering the charged Riemannian Penrose inequality.
