AI 中文总结
该研究提出相对论框架计算黑洞时空中有质量标量场本征谱修正，对比微扰与非微扰结果，指出双星伴星对超辐射的强影响，呼吁重新审视超辐射终止的相关估计。
AI 中文摘要
我们提出了一种相对论框架，用于计算受扰动黑洞时空中有质量标量场的本征频率谱修正，包括衰变率的一阶频移和二阶模式混合效应。我们还阐明了非相对论处理的适用范围，证明了基于完备性的描述精度有限，凸显了该谱的非厄米性质。以星系晕和吸积盘作为具有物理动机的扰动，我们将相对论微扰预测的本征频率频移与非微扰数值解进行了基准对比。我们还给出了由双星伴星诱导的一阶相对论本征频率频移，其对旋转黑洞周围有质量标量场的超辐射动力学可能产生更强影响，这推动了未来的专门分析。我们的结果表明，应在相对论框架内重新审视此前关于双星伴星和吸积盘导致超辐射终止的估计。
英文摘要
We present a relativistic framework for computing corrections to the eigenfrequency spectrum of a massive scalar field in perturbed black-hole spacetimes, including first-order shifts to decay rates and second-order mode-mixing effects. We also clarify the regime of validity of non-relativistic treatments and show that the accuracy of completeness-based descriptions is limited, highlighting the non-Hermitian nature of the spectrum. Using galactic halos and accretion disks as physically motivated perturbations, we benchmark the relativistic perturbative predictions to the eigenfrequency shifts against non-perturbative numerical solutions. We also present first-order relativistic eigenfrequency shifts induced by binary companions, whose potentially stronger impact on superradiant dynamics of massive scalar fields around spinning black holes motivates future dedicated analyses. Our results suggest that previous estimates of the termination of superradiance due to binary companions and disks should be revisited within a relativistic framework.
Comments19 pages, 9 figures
