论文标题
黑洞准确模式的意义：仔细的外观
Significance of Black Hole Quasinormal Modes: A Closer Look
论文作者
论文摘要
众所周知，使用阶梯函数近似regge-wheeler势会显着修改Schwarzschild黑洞准模式光谱。令人惊讶的是，频谱中的这种变化对Ringdown波形的影响很小。我们检查了这个问题是否是由跳跃不连续性和/或步骤函数的分段恒定性质引起的。我们表明，用连续的分段线性函数替换步骤函数不会改变结果。但是，与先前发表的结果相反，我们发现使用步骤函数或分段线性函数可以将RINGDOWN波形近似为任意精度。因此，这个近似过程提供了一种新的数学工具来计算环down波形。另外，与正常模式相似，近似电势的准模式似乎形成了一个完整的集合，该集合描述了Ringdown波形的整个时间演变。我们还研究了可以准确计算出准式模式的Regge-wheeler电位的更平滑近似，以更好地了解准模式频谱的各个区域的不同部分如何影响。
It is known that approximating the Regge-Wheeler Potential with step functions significantly modifies the Schwarzschild black hole quasinormal mode spectrum. Surprisingly, this change in the spectrum has little impact on the ringdown waveform. We examine whether this issue is caused by the jump discontinuities and/or the piecewise constant nature of step functions. We show that replacing the step functions with a continuous piecewise linear function does not qualitatively change the results. However, in contrast to previously published results, we discover that the ringdown waveform can be approximated to arbitrary precision using either step functions or a piecewise linear function. Thus, this approximation process provides a new mathematical tool to calculate the ringdown waveform. In addition, similar to normal modes, the quasinormal modes of the approximate potentials seem to form a complete set that describes the entire time evolution of the ringdown waveform. We also examine smoother approximations to the Regge-Wheeler potential, where the quasinormal modes can be computed exactly, to better understand how different portions of the potential impact various regions of the quasinormal mode spectrum.
