AI 中文总结
研究广义纳里艾时空中标量场和麦克斯韦场与爱因斯坦张量耦合的准正则模，通过分析耦合引入的临界值及对场振荡部分的影响，揭示相同曲率耦合对两种场微扰的不同作用方式。
AI 中文摘要
我们研究了广义纳里艾时空中与爱因斯坦张量耦合的标量场和麦克斯韦场微扰的准正则模。结果表明，对于这两种微扰类型，耦合引入了不同的临界值，将频谱分为不同分支。在这些临界值附近，决定\(\omega_R^2\)的平方根项可能改变符号，产生模式为纯虚数的参数区间。远离此区域时，耦合以相反方式影响两个场的振荡部分：对标量场，\(\omega_R^2\)通常随耦合常数\(\eta\)增加，而对麦克斯韦场则随\(\eta\)减小。磁荷倾向于增强振荡响应，增加时空维数会缩小纯虚数区域。这种比较分析表明相同的曲率耦合会以定性不同的方式影响标量和麦克斯韦微扰。
英文摘要
We investigate the quasinormal modes of scalar and Maxwell field perturbations coupled to the Einstein tensor in generalized Nariai spacetimes. Our results show that, for both types of perturbations, the coupling introduces different critical values, which separate the frequency spectrum into distinct branches. Near these critical values, the square-root term that determines $ω_R^2$ may change sign, giving rise to a parameter interval in which the modes are purely imaginary. Away from this regime, the coupling affects the oscillatory parts of the two fields in opposite ways: $ω_R^2$ generally increases with the coupling constant $η$ for the scalar field, whereas it decreases with $η$ for the Maxwell field. The magnetic charge tends to enhance the oscillatory response, while increasing the spacetime dimension narrows the purely imaginary regime. This comparison shows analytically that the same curvature coupling can affect scalar and Maxwell perturbations in qualitatively different ways.
