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arXiv 0908.1664gr-qcastro-ph.HE
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极端质量比吸气中的引力自作用力

Gravitational self force in extreme mass-ratio inspirals

Leor Barack

摘要:

本文讨论了大质量粒子在大黑洞轨道上的引力自作用力。从具有极端质量比的强引力双星中探测到引力波的前景,重新激发了人们对这个老问题的兴趣。本文首先概述弯曲时空中引力自相互作用理论的最新进展,然后探讨在粒子绕克尔黑洞运行的情况下,为实现这一理论而设计的一些思想和计算策略。我们详细审查这些方法中的两个:(一)标准的模式和方法,其中的度量扰动是正规化模式的多极分解,及(二)$m$模式正规化,从而个别方位角模式的度量扰动正规化在2+1维。我们讨论了几个实际问题,包括规范的选择,粒子奇异性的数值表示,以及如何在频域计算中处理粒子附近的高频贡献。作为一个完整的端到端实现的模式和方法的例子,我们讨论的偏心测地线轨道在史瓦西的引力自作用力的计算,使用直接集成的洛伦兹规范扰动方程在时域中。随着计算框架的建立,研究人员最近开始探索引力自作用力的物理后果;我们将描述这一领域的一些初步结果。这篇评论的附录第一次详细推导了在克尔时空中实现模和方法所需的正则化参数。

英文摘要:

This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, and proceed to survey some of the ideas and computational strategies devised for implementing this theory in the case of a particle orbiting a Kerr black hole. We review in detail two of these methods: (i) the standard mode-sum method, in which the metric perturbation is regularized mode-by-mode in a multipole decomposition, and (ii) $m$-mode regularization, whereby individual azimuthal modes of the metric perturbation are regularized in 2+1 dimensions. We discuss several practical issues that arise, including the choice of gauge, the numerical representation of the particle singularity, and how high-frequency contributions near the particle are dealt with in frequency-domain calculations. As an example of a full end-to-end implementation of the mode-sum method, we discuss the computation of the gravitational self-force for eccentric geodesic orbits in Schwarzschild, using a direct integration of the Lorenz-gauge perturbation equations in the time domain. With the computational framework now in place, researchers have recently turned to explore the physical consequences of the gravitational self force; we will describe some preliminary results in this area. An appendix to this review presents, for the first time, a detailed derivation of the regularization parameters necessary for implementing the mode-sum method in Kerr spacetime.

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