标题： 修改引力理论中的黑洞扰动 显示英文标题

标题： Black hole perturbations in modified gravity theories

摘要： 最近对双黑洞合并产生的引力波（GWs）的首次探测激发了人们对广义相对论（GR）可能偏离的兴趣，因为这些偏离可能在这些系统发出的GWs中被探测到。特别值得关注的是双黑洞合并的回音阶段，该阶段可以通过关于背景静态黑洞解的线性扰动来描述。这些扰动主要对应于“准正则模”（QNMs）的叠加，其频率形成一个离散集。人们预期修改的引力模型可能会预测与GR对应的QNMs不同的QNMs：对GW信号的详细分析为测试GR和寻找修改引力的具体特征提供了无价的窗口。本论文的工作是在标量-张量引力理论，特别是退化的高阶标量-张量理论的背景下进行的。我们首先回顾这些理论及其特性，并描述一种将它们重新表述为具有清晰几何解释框架的方法。然后，我们研究了这些理论中几个现有非旋转黑洞解的线性扰动，并说明为什么通常情况下得到的扰动方程很难解耦。在奇宇称扰动的情况下，当有可能时，我们描述波的传播并将其与底层时空的稳定性联系起来。当不可能时，我们通过使用数学文献中最近提出的一种算法来克服这一困难，该算法允许我们在黑洞视界和无限远处解耦方程。这使我们能够获得此类时空上波的渐近行为，提供有价值的信息，可以帮助排除其中一些情况。最后，我们利用获得的渐近行为数值计算QNMs。 显示英文摘要

摘要： The recent first detection of gravitational waves (GWs) from binary black hole mergers has spurred a renewed interest in possible deviations from General Relativity (GR), since they could be detected in the GWs emitted by such systems. Of particular interest is the ringdown phase of a binary black hole merger, which can be described by linear perturbations about a background stationary black hole solution. These perturbations mainly correspond to a superposition of 'quasi-normal modes' (QNMs), whose frequencies form a discrete set. One expects that modified gravity models could predict QNMs that differ from their GR counterpart: the detailed analysis of the GW signal represents an invaluable window to test GR and to look for specific signatures of modified gravity. The work done in this thesis takes place in the context of scalar-tensor theories of gravity, and more particularly the Degenerate Higher-Order Scalar-Tensor theories. We start by a review of these theories and their properties, and describe a way to reformulate them in a framework with a clear geometrical interpretation. We then study linear perturbations about several existing nonrotating black hole solutions of such theories, and show why the perturbation equations obtained are very hard to decouple in general. When it is possible, in the case of odd parity perturbations, we describe the propagation of waves and relate it to the stability of the underlying spacetime. When it is not, we circumvent the difficulty by making use of an algorithm proposed recently in the mathematical literature that allows us to decouple the equations both at the black hole horizon and at infinity. This allows us to get the asymptotic behaviour of waves on such spacetimes, yielding valuable information that can allow us to rule some of them out. Finally, we use the asymptotic behaviours obtained to compute QNMs numerically.