标题： 准正则模和黑洞相变中的非线性电动力学 显示英文标题

标题： Quasi-Normal Modes and Nonlinear Electrodynamics in Black Hole Phase Transitions

摘要： 我们研究在$F(R)$-Euler-Heisenberg引力框架下，带电黑洞中热力学相变与准正则模（QNMs）之间的联系。非线性电磁场导致丰富的热力学相结构，并显著影响无质量标量场的QNMs。通过分析QNMs谱，我们发现标记QNMs斜率参数$K$发散消失的转变点与由比热描述的热力学相结构变化一致，在计算不确定性范围内。这种精确匹配在曲率参数和电荷变化时仍然成立。此外，我们表明较大的角量子数$l$会削弱这种对应关系，而较高的泛音数$n$在超过某个阈值后会恢复这种对应关系。这些发现表明黑洞的热力学相变包含动态信息，揭示了黑洞热力学和动力学性质之间的基本联系。 显示英文摘要

摘要： We investigate the connection between thermodynamic phase transitions and quasi-normal modes (QNMs) in charged black holes with a positive curvature constant, within the framework of $F(R)$-Euler-Heisenberg gravity. Nonlinear electromagnetic fields lead to rich thermodynamic phase structures and significantly affect the QNMs of massless scalar fields. By analyzing the QNMs spectrum, we find that the transition point marking the disappearance of divergence in the QNMs slope parameter $K$ aligns with the change of the thermodynamic phase structure described by the heat capacity, within the bounds of computational uncertainty. This precise matching holds under variations of curvature parameters and charge. Furthermore, we show that larger angular quantum number $l$ diminishes this correspondence, while higher overtone number $n$ restores it beyond a threshold. These findings demonstrate that thermodynamic phase transitions of black holes carry embedded dynamical information, uncovering a fundamental link between black hole thermodynamic and dynamical properties.