论文标题
引力波对黑洞的非线性扰动。 ii。准模式和紧凑问题
The non-linear perturbation of a black hole by gravitational waves. II. Quasinormal modes and the compactification problem
论文作者
论文摘要
最近，弗里德里希（Friedrich）的广义保形场方程（GCFE）已被数值实施，邦迪能量和邦迪 - 萨基斯质量损失等全球量已成功地直接在零侵占上计算出来。尽管是通过局部差别几何方法研究全球量的有吸引力的选择，但在物理时空中研究数量的GCFE的可行性如何？特别是，需要准确解决的恒定适当的物理时间段的演化轨道现象可以多长时间？我们通过研究通过非线性重力扰动在Schwarzschild时空引起的曲率振荡来解决这个问题。对于足够小的幅度，这些是由线性准模式近似的，其中每个模式以仅由Schwarzschild质量确定的频率响起。我们发现，GCFE确实可以解决这些振荡，从而快速接近线性状态，但是只有在紧凑型``太快''才能以数值处理之前很短。
Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity. Although being an attractive option for studying global quantities by way of local differential geometrical methods, how viable are the GCFE for study of quantities arising in the physical space-time? In particular, how long can the evolution track phenomena that need a constant proper physical timestep to be accurately resolved? We address this question by studying the curvature oscillations induced on the Schwarzschild space-time by a non-linear gravitational perturbation. For small enough amplitudes, these are the well approximated by the linear quasinormal modes, where each mode rings at a frequency determined solely by the Schwarzschild mass. We find that the GCFE can indeed resolve these oscillations, which quickly approach the linear regime, but only for a short time before the compactification becomes ``too fast'' to handle numerically.
