标题： 黑洞旋停阶段的非线性效应 显示英文标题

标题： Nonlinearities in Black Hole Ringdowns

摘要： 由扰动黑洞（BH）衰减产生的引力波应变通常使用一阶黑洞扰动理论进行解析建模。 在本文中，我们表明为了对黑洞合并模拟的衰减阶段进行建模，需要考虑二阶效应。 专注于 $(\ell,m)=(4,4)$ 角向谐波，我们发现存在一个二次效应，在一系列双黑洞质量比下与理论预期一致。 我们发现二次 $(4,4)$ 模式的振幅与基本 $(2,2)$ 模式——其父模式——呈二次比例关系。 非线性模式的振幅与线性 $(4,4)$ 模式的振幅相当甚至更大。 因此，正确建模高阶谐波的衰减——将模式不匹配改善多达两个数量级——需要包含非线性效应。 显示英文摘要

摘要： The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain's $(\ell,m)=(4,4)$ angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic $(4,4)$ mode's amplitude exhibits quadratic scaling with the fundamental $(2,2)$ mode -- its parent mode. The nonlinear mode's amplitude is comparable to or even larger than that of the linear $(4,4)$ mode. Therefore, correctly modeling the ringdown of higher harmonics -- improving mode mismatches by up to 2 orders of magnitude -- requires the inclusion of nonlinear effects.