标题： 脉动恒星的引力波：相对论恒星扰动方程的演化 显示英文标题

标题： Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star

摘要： 我们考虑相对论星体的扰动作为初始值问题。 在详细讨论了问题的表述（扰动方程和星体中心及表面的适当边界条件）之后，我们从几组不同的初始数据出发对这些方程进行数值演化。 在所有考虑的情况下，我们发现产生的引力波携带了星体若干脉动模式的特征。 通常，流体$f$模式、前两个$p$模式以及衰减最慢的引力$w$模式会出现在信号中。 这表明脉动模式可能是来自碰撞中子星或超新星的可探测引力波的一个有趣来源。 我们还综述了文献，并发现旋转核心坍缩和中子星并合的数值模拟中存在若干模式存在的迹象。 如果未来引力波天线能够探测到这些模式信号，人们有望推断出关于中子星的详细信息。 由于扰动演化应能充分描述动态激发的中子星的后期行为，因此本工作也可以作为未来全非线性模拟的基准测试。 显示英文摘要

摘要： We consider the perturbations of a relativistic star as an initial-value problem. Having discussed the formulation of the problem (the perturbation equations and the appropriate boundary conditions at the centre and the surface of the star) in detail we evolve the equations numerically from several different sets of initial data. In all the considered cases we find that the resulting gravitational waves carry the signature of several of the star's pulsation modes. Typically, the fluid $f$-mode, the first two $p$-modes and the slowest damped gravitational $w$-mode are present in the signal. This indicates that the pulsation modes may be an interesting source for detectable gravitational waves from colliding neutron stars or supernovae. We also survey the literature and find several indications of mode presence in numerical simulations of rotating core collapse and coalescing neutron stars. If such mode-signals can be detected by future gravitational-wave antennae one can hope to infer detailed information about neutron stars. Since a perturbation evolution should adequately describe the late time behaviour of a dynamically excited neutron star, the present work can also be used as a bench-mark test for future fully nonlinear simulations.