论文标题
旋转外来紧凑物体的潮汐响应和接近马的边界条件
Tidal response and near-horizon boundary conditions for spinning exotic compact objects
论文作者
论文摘要
$ | s | = 2 $的Teukolsky方程提供了有效的方法来解决Kerr黑洞周围的曲率扰动。对这些扰动的未来（过去）地平线对这些扰动施加规律性条件对应于施加即将进行的（外向）波边界条件。但是，对于具有外部Kerr时空的外来紧凑型物体（ECO），尚不清楚如何在其边界上物理施加曲率扰动的边界条件。我们使用膜范式考虑了一个信托观察家（FIDOS），该家族在线性扰动的Kerr Black Hole的地平线上方，解决了这个问题。从这些观察者的参考框架来看，ECO将由于即将进行的引力波，对这些波的反应并产生外流波。事实证明，如果即将进行和即将进行的波浪在地平线附近都存在，那么Newman Penrose（NP）数量$ψ_0$将在数值上由正在进行的波浪统治，而NP数量$ψ_4$将由即将到来的波浪主导。这样，我们以$ψ_0$与$ψ_4$之间关系的形式获得了生态边界条件，这是由Eco在FIDO框架中的潮汐响应确定的方式。我们探索了几种修改FIDO框架中重力波散分散的方法，并推断出Teukolsky函数的相应的Eco边界条件。随后，我们仅获得$ψ_4$的边界条件，以及Sasaki-Nakamura和Detweiler的功能。事实证明，旋转ECO的反射通常会在扰动场的不同$ \ ell $组件之间混合，并且对于具有不同奇偶族的扰动而言是不同的。我们还将边界条件应用于旋转ECO的计算重力波回波，并求解旋转ECOS的准正常模式。
Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to in-going gravitational waves, respond to these waves, and generate out-going waves. As it also turns out, if both in-going and out-going waves exist near the horizon, the Newman Penrose (NP) quantity $ψ_0$ will be numerically dominated by the in-going wave, while the NP quantity $ψ_4$ will be dominated by the out-going wave. In this way, we obtain the ECO boundary condition in the form of a relation between $ψ_0$ and the complex conjugate of $ψ_4$, in a way that is determined by the ECO's tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame, and deduce the corresponding ECO boundary condition for Teukolsky functions. We subsequently obtain the boundary condition for $ψ_4$ alone, as well as for the Sasaki-Nakamura and Detweiler's functions. As it also turns out, reflection of spinning ECOs will generically mix between different $\ell$ components of the perturbations fields, and be different for perturbations with different parities. We also apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and solve for the spinning ECOs' quasi-normal modes.
