标题： 球对称情况下广义相对论之外的修正Teukolsky形式主义的通用方法 显示英文标题

标题： Generic Modified Teukolsky Formalism beyond General Relativity for Spherically Symmetric Cases

摘要： 引力波的观测开启了利用强场、非线性区域检验引力理论的新时代。 在双黑洞合并的回响阶段以及极端质量比吸积过程中发射的引力波，对黑洞的性质特别敏感，这使得它们对于探测广义相对论偏差至关重要。 这些研究需要一个超越广义相对论的黑洞扰动理论的坚实基础。 虽然现有的研究已经利用了黑洞扰动理论来探索超越广义相对论的修改，但它们通常集中于特定的替代理论或量子引力的唯象模型。 在这篇论文中，我们建立了一个修正的解耦Teukolsky形式主义，它广泛适用于球对称时空，而无需预先设定引力拉格朗日量。 该形式主义使用Newman-Penrose框架，通过由Weyl标量表征的曲率扰动来容纳超越广义相对论的一类更广泛的时空。 我们的方法正确处理了非Ricci平坦背景，并避免了与其他修正的Teukolsky形式主义中存在的有效势相关的微妙分析问题。 显示英文摘要

摘要： The observation of gravitational waves has inaugurated a new era for testing gravitational theories in strong-field, nonlinear regimes. Gravitational waves emit during the ringdown phase of binary black hole mergers and from extreme mass ratio inspirals are particularly sensitive to the properties of black holes, making them crucial for probing deviations from general relativity. These studies need a robust foundation in black hole perturbation theory beyond general relativity. While existing studies have employed black hole perturbation theories to explore modifications beyond general relativity, they often focus on specific alternative theories or phenomenological models of quantum gravity. In this paper, we establish a modified decoupled Teukolsky formalism that is broadly applicable to spherically symmetric spacetimes without requiring a predetermined gravitational Lagrangian. This formalism uses the Newman-Penrose framework, which utilizes curvature perturbations characterized by Weyl scalars, to accommodate a wider class of spacetimes beyond general relativity. Our approach correctly handles non-Ricci-flat backgrounds and circumvents subtle analytical issues associated with effective potentials that are present in other modified Teukolsky formalisms.