极值爱因斯坦-双麦克斯韦-膨胀子分支上的吸引与排斥
Attraction and repulsion along extremal Einstein--two-Maxwell--dilaton branches
AI总结：
研究四维爱因斯坦-膨胀子-双麦克斯韦系统中极值质量分支的唯一性，证明电荷比线上存在唯一正解析解，并揭示吸引与排斥随耦合参数转变的规律。
AI中文摘要：
我们研究了四维爱因斯坦引力与一个膨胀子及两个具有相反符号膨胀子耦合的麦克斯韦场耦合时的极值质量分支。对于一般耦合，极值质量由一阶非线性方程控制，该方程没有已知的闭式解。我们证明该方程在全实电荷比直线上存在唯一的正$C^2$解，且该解是实解析的，因此整个正电荷锥上的正性选择出唯一的全局质量分支。沿此分支，任意两个不成比例的正电荷向量在$ab>-1$时相互吸引，在$ab=-1$时前导力消失，在$ab<-1$时相互排斥。同一转变确定了极值质量面的横向凸性以及任意有限正电荷划分下质量差的符号。该符号定理通过已知的维度重标度扩展到更高维度。径向重构随后表明，质量分支上的每个点都定义了一个渐近平坦的外部，其内端点具有有限面积，而光滑或解析视界延伸则是限制耦合和标量流的单独条件。
英文摘要：
We study extremal mass branches in four-dimensional Einstein gravity coupled to one dilaton and two Maxwell fields with opposite-sign dilaton couplings. For generic couplings the extremal mass is governed by a nonlinear first-order equation with no known closed-form solution. We prove that this equation has a unique positive $C^2$ solution on the full real charge-ratio line and that the solution is real analytic, so positivity on the entire positive charge cone selects a unique global mass branch. Along this branch, any two nonproportional positive charge vectors attract for $ab>-1$, have vanishing leading force at $ab=-1$, and repel for $ab<-1$. The same transition fixes the transverse convexity of the extremal mass surface and the sign of the mass difference under arbitrary finite positive-charge partitions. The sign theorem extends to higher dimensions through the known dimensional rescaling. A radial reconstruction then shows that every point of the mass branch defines an asymptotically flat exterior with a finite-area inner endpoint, while smooth or analytic horizon extension is a separate condition that restricts the couplings and scalar flow.
