标题： 反德西特时空中的非线性电磁场黑洞自发标量化的动力学 显示英文标题

标题： Dynamics of spontaneous scalarization of black holes with nonlinear electromagnetic fields in anti-de Sitter spacetime

摘要： 我们研究了具有渐近AdS边界条件的爱因斯坦-Born-Infeld-标量（EBIS）模型中的自发标量化现象，揭示了黑洞演化中新的动力学临界现象。通过数值分析，我们发现了一种独特的“翻转”现象，其中标量场在不同稳定构型之间表现出临界跃迁。这些跃迁以两种形式表现出来：初始扰动振幅或标量-电磁耦合变化下的单次翻转，以及黑洞电荷变化下的双次翻转。在临界点附近，系统显示出普遍的弛豫行为，其弛豫时间遵循对数尺度关系$\tau \propto \ln |p - p_s|$，其中$p_s$表示临界初始振幅。我们证明，这些跃迁源于系统接近不稳定AdS-Born-Infeld黑洞构型的过程，这些构型作为不同稳定相之间的分隔面。Born-Infeld参数在此动力学中起关键作用，在强非线性极限下标量毛发消失。这些结果揭示了具有非线性电磁耦合理论中黑洞相变的基本方面，并为引力系统中的临界现象提供了新的见解。 显示英文摘要

摘要： We investigate spontaneous scalarization in the Einstein-Born-Infeld-Scalar (EBIS) model with asymptotically AdS boundary conditions, revealing novel dynamical critical phenomena in black hole evolution. Through numerical analysis, we discover a distinctive ``flip" phenomenon where the scalar field exhibits critical transitions between different stable configurations. These transitions manifest in two forms: a single flip under variations in initial perturbation amplitude or scalar-electromagnetic coupling, and a double flip when varying black hole charge. Near critical points, the system displays universal relaxation behavior characterized by logarithmic scaling of relaxation time, $\tau \propto \ln |p - p_s|$, where $p_s$ denotes the critical initial amplitude. We demonstrate that these transitions arise from the system's approach to unstable AdS-Born-Infeld black hole configurations, which serve as separatrices between distinct stable phases. The Born-Infeld parameter plays a crucial role in this dynamics, with scalar hair vanishing in the strong nonlinearity limit. These results reveal fundamental aspects of black hole phase transitions in theories with nonlinear electromagnetic couplings and provide new insights into critical phenomena in gravitational systems.