基于Stokes几何的Kerr黑洞准正规模式的激发区域
Excitation region of Kerr black hole quasinormal modes from Stokes geometry
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中文总结 AI 辅助
该研究从解析和数值角度，结合Stokes几何与QNM加尾展开收敛测试，确定Kerr黑洞QNM激发半径，发现其与泛音数相关，极端极限下趋近外视界。
中文摘要 AI 辅助
我们从解析和数值两个角度研究黑洞准正规模式（QNMs）的激发区域。在解析方面，我们提出QNM激发半径由WKB解在反Stokes线处的主导权切换确定，基于该图像推导了Kerr时空中QNM激发半径的条件；在质量为M的Schwarzschild极限下，我们得到了此前已知的r=2.556929 M，其与光球半径r=3M不同，还证明高泛音极限下激发半径与角模式ℓ无关。作为独立方法，我们采用QNM加尾展开的数值收敛性测试，在低自旋和中等自旋的高泛音极限下得到与Stokes几何一致的结果；在极端极限下，QNM收敛半径趋近于外视界，这由零阻尼模式的Stokes几何而非高泛音极限描述，与极端极限下振铃由零阻尼模式主导的事实一致。基于Stokes几何与收敛测试的互补分析，我们认为一般情况下QNM激发半径取决于QNM泛音数，从而产生有效QNM收敛区域。
英文摘要
We investigate the excitation region of black hole quasinormal modes (QNMs) from both analytical and numerical perspectives. On the analytical side, we propose that the QNM excitation radius is identified by the dominance switching of WKB solutions across an anti-Stokes line. Based on this picture, we derive the condition for the QNM excitation radius in Kerr spacetime. In the Schwarzschild limit with mass $M$, we reproduce the previously known value $r=2.556929 M$, which differs from the light ring radius $r=3M$. We also show that the excitation radius is independent of the angular mode $\ell$ in the high-overtone limit. As an independent approach, we employ the numerical convergence test of QNM-plus-tail expansion and obtain values consistent with the Stokes geometry in the high-overtone limit at low and intermediate spins. In the extremal limit, the QNM convergence radius approaches the outer horizon, which is captured by the Stokes geometry of the zero-damping modes, rather than the high-overtone limit. This is consistent with the fact that the ringdown is dominated by zero-damping modes in the extremal limit. Based on the complementary analysis of Stokes geometry and the convergence test, we argue that in general, the QNM excitation radius depends on the QNM overtone number, giving rise to an effective QNM convergence region.
