爱因斯坦-麦克斯韦-标量黑洞中的Kasner临界标度：非线性坍缩与标量化
Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization
- Huazhong University of Science and Technology（华中科技大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究证明爱因斯坦-麦克斯韦-标量黑洞中Kasner临界标度指数非普适，通过调节高阶耦合可实现$1/(2m)$指数，并明确前置因子，建立指数层级。
AI中文摘要：
一项数值研究曾观察到渐近平坦标量化黑洞的Kasner参数具有$1/2$的临界标度指数，并推测该指数具有普适性[Phys.\\ Rev.\\ Lett.\\ \textbf{136}, 251402 (2026)]。在相同的静态、球对称爱因斯坦-麦克斯韦-标量设定中，我们证明该指数并非普适。我们发展了一个严格的数学框架，并通过在固定二次耦合参数$\mu$下调节高阶项，构造了实现任意整数$m\ge1$的指数$1/(2m)$的耦合。非线性内部坍缩产生类空的Kasner奇点，其中$\beta_{\rm K}\propto\varepsilon^{-1}$，$\varepsilon$为事件视界处标量场的值。因此，满足$q/q_\star-1\propto\varepsilon^{2m}$的外部分支给出$\beta_{\rm K}\propto|q/q_\star-1|^{-1/(2m)}$，其中$q$为荷质比，$q_\star$为其临界值。我们还明确确定了前置因子。这恢复了$1/2$定律，并建立了包括$1/4$和$1/6$在内的指数层级。
英文摘要：
A critical scaling exponent of $1/2$ was numerically observed for the Kasner parameter of asymptotically flat scalarized black holes and conjectured to be universal [Phys.\ Rev.\ Lett.\ \textbf{136}, 251402 (2026)]. In the same static, spherically symmetric Einstein--Maxwell--scalar setting, we show that this exponent is not universal. We develop a rigorous mathematical framework and construct couplings realizing exponents $1/(2m)$ for any integer $m\ge1$ by tuning higher-order terms at fixed quadratic coupling parameter $μ$. Nonlinear interior collapse produces a spacelike Kasner singularity with $β_{\rm K}\propto\varepsilon^{-1}$, where $\varepsilon$ is the value of scalar field at the event horizon. An exterior branch satisfying $q/q_\star-1\propto\varepsilon^{2m}$, therefore, yields $β_{\rm K}\propto|q/q_\star-1|^{-1/(2m)}$, where $q$ is the charge-to-mass ratio and $q_\star$ its critical value. We also determine the prefactor explicitly. This recovers the $1/2$ law and establishes a hierarchy including $1/4$ and $1/6$.
