黑洞准正则模的薛定谔微扰理论
Schrödinger perturbation theory for black hole quasinormal modes
- Nottingham Centre of Gravity & School of Mathematical Sciences, University of Nottingham（诺丁汉大学引力中心与数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究黑洞准正则模因偏离真空广义相对论产生的频移，利用双线性形式将薛定谔微扰理论用于黑洞，获任意阶频移公式及一阶模移谱分解，通过实例说明框架，揭示QNM和发散。
AI中文摘要：
偏离真空广义相对论（如修正理论或存在环境）会使黑洞准正则模（QNM）谱产生微小偏移，这对引力波天文学愈发重要。一阶频移已明晰，但尚无计算高阶修正的系统框架。主要障碍是系统非自伴性致QNMs非完备基。不过，近期表明QNMs关于适当双线性形式正交。本文利用双线性形式将薛定谔微扰理论系统提升至黑洞情形，得到任意阶准正则频移公式，给出一阶模移的谱分解，以缓慢旋转的克尔和普施尔 - 特勒例子说明该框架，发现QNM和发散。
英文摘要：
Deviations from vacuum general relativity (such as modified theories or the presence of an environment) produce small shifts in black hole quasinormal mode (QNM) spectra. These effects are becoming increasingly relevant for gravitational wave astronomy as observations of ringdown spectra become more precise. To leading order in deviations from vacuum general relativity, frequency shifts can be calculated using eigenvalue perturbation theory. However, for Kerr, there is no systematic framework to compute higher order corrections. The major obstacle is that QNMs do not form a complete basis due to the non-self-adjointness of the system. Nevertheless, it was recently shown that QNMs are orthogonal with respect to an appropriate bilinear form. In this work, we use the bilinear form to systematically lift Schrödinger perturbation theory to the black hole setting. We obtain a formula for quasinormal frequency shifts to any order, in terms of lower order mode shifts. We also provide a spectral decomposition of the first-order mode shift, which involves projections onto unperturbed QNMs along with continuous-spectrum contributions---making incompleteness explicit. We illustrate the framework on slowly-spinning Kerr and Pöschl-Teller examples, where we find that the QNM sum itself diverges.
