Synergistic approach to the two-body problem in General Relativity: black-hole binaries in the intermediate mass-ratio regime

该项目解决了中等质量比区域（1：100 - 1：1000）中黑洞内部粒子的动力学和引力波特征建模问题。对于更极端的质量比，黑洞微扰理论提供了足够的描述，而在可比质量的情况下，数值相对论已经非常成功。但当质量比为中间值时，两者都不起作用。由于目前和未来的引力波实验并非不可能观察到这种中等质量比的螺旋，它们的建模仍然是引力波物理学中一个重要的开放问题。 在这个项目中，我们建议通过结合黑洞微扰和数值相对论技术来解决这个问题。这项研究将与德国的阿尔伯特爱因斯坦研究所（马克斯普朗克引力物理研究所）的领先数值相对论小组合作完成。这个想法是通过将小物体附近的近似解析解与其他地方的完全非线性数值解相匹配，为双星的时空构建一个足够精确的完整爱因斯坦场方程解。实际上，小物体附近的一个区域是“切除”的，切除边界条件是使用微扰方法解析得出的。其效果将是部分缓解阻碍数值计算效率的尺度差异。 我们计划开始研究一个相对简单的1+1维线性标量场模型。一旦我们确信我们的切除程序工作良好，我们将努力将类似的策略应用于3+1维的引力问题，在这个阶段，我们将与AEI小组合作。该计划是将我们的新切除方法纳入现有的SpEC平台（该平台已经为LIGO-Virgo合作产生了精确的波形，目前质量比高达1：10）。

This project tackles the problem of modelling the dynamics and gravitational-wave signature of black-hole insiprals in intermediate mass-ratio regime (1:100 - 1:1000). For more extreme mass ratios, black hole perturbation theory provides a sufficient description, whilst in the case of comparable masses numerical relativity has been very successful. But neither works well when the mass ratio is intermediate. Since current and future gravitational-wave experiments are not unlikely to observe such intermediate mass-ratio inspirals, their modelling remains an important open problem in gravitational-wave physics. In this project we propose to tackle the problem through a combination of black-hole perturbation and numerical relativistic techniques. The research will be done in collaboration with the leading numerical-relativity group at the Albert Einstein Institute (Max Planck Institute for Gravitational Physics) in Germany. The idea is to construct a sufficiently accurate solution of the full Einstein Field Equations for the binary's spacetime by matching an approximate analytical solution near the small object to a fully nonlinear numerical solution elsewhere. In effect, a region near the small object is ``excised'', with excision boundary conditions derived analytically using perturbative methods. The effect will be to partially relieve the scale disparity that impedes the efficiency of the numerical calculation. We plan to begin by studying a relatively simple linear scalar-field model in 1+1 dimensions. Once we are confident that our excision procedure works well, we will endeavourer to apply a similar strategy to the gravitational problem in 3+1 dimensions, at which stage we will collaborate with the AEI group. The plan is to incorporate our new excision method into the existing SpEC platform (which already produces accurate waveforms for the LIGO-Virgo Collaboration, currently for mass ratios up to ~1:10).