基于束缚态和同伦形变的准正则模新方法
A New Method for Quasinormal Modes From Bound States and Homotopy deformations
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中文总结 AI 辅助
该研究提出一种计算准正则模的新束缚态方法，可直接从史瓦西黑洞反转Regge-Wheeler势的束缚态谱数值计算QNM频率，经同伦形变改进后可计算更多高阶泛音模。
中文摘要 AI 辅助
受Mashhoon的束缚态方法启发，我们提出了一种计算准正则模（QNMs）的新束缚态方法。通过引入实参数α的两步坐标变换，将QNM问题映射为束缚态问题，其本征值Eₙ(α)通过解析延拓逆映射为QNM频率ωₙ。利用该方法，我们首次直接从反转Regge-Wheeler势的束缚态谱数值计算了史瓦西黑洞的多种QNM频率。研究发现，该方法对于泛音n≤ℓ（ℓ为多极矩数）的低阶模能产生高精度的QNM频率，而对于更高阶泛音，精度会降低或计算失败。为明确该局限性的起源，我们在复α平面中利用帕德逼近分析了本征值Eₙ(α)的奇点结构。对于高阶泛音，Eₙ(α)的奇点位于解析延拓圆内，为该方法的局限性提供了直接解释。为缓解这一局限性，我们建议对势进行同伦形变，这一改进使我们能够可靠计算更多高阶泛音模。
英文摘要
Inspired by Mashhoon's bound state method, we propose a new bound state method for computing quasinormal modes (QNMs). By a two-step coordinate transformation where a real parameter $α$ is introduced, a QNM problem is mapped to a bound state problem, whose eigenvalues $E_n(α)$ are inversely mapped to the QNM frequencies $ω_n$ via analytic continuation. With this method, we numerically calculate various QNM frequencies for a Schwarzschild black hole directly from the bound state spectrum of the inverted Regge-Wheeler potential for the first time. It is found that the method yields QNM frequencies of high accuracy for low-lying modes with overtone $n\leq\ell$ ($\ell$ is the multipole number), while the accuracy degrades or the calculation fails for higher overtones. To identify the origin of this limitation, we analyze the singularity structure of the eigenvalues $E_n(α)$ using Padé approximants in the complex $α$-plane. For higher overtones, the singularities of $E_n(α)$ lie within the analytic continuation circle, providing a direct explanation for the limitation of the method. To mitigate this limitation, we suggest a homotopy deformation to the potential, which improves the method and enable us to compute a few more high overtone modes reliably.
