The detection of gravitational waves from binary black-hole mergers by the LIGO-Virgo Collaboration marks the dawn of an era when general-relativistic dynamics in its most extreme manifestation is directly accessible to observation. In the future, planned (space-based) observatories operating in the millihertz band will detect the intricate gravitational-wave signals from the inspiral of compact objects into massive black holes residing in galactic centers. Such inspiral events are extremely effective probes of black-hole geometries, offering unparalleled precision tests of general relativity in its most extreme regime. This prospect has in the past two decades motivated a programme to obtain an accurate theoretical model of the strong-field radiative dynamics in a two-body system with a small mass ratio. The problem naturally lends itself to a perturbative treatment based on a systematic expansion of the field equations in the small mass ratio. At leading order one has a pointlike particle moving in a geodesic orbit around the large black hole. At subsequent orders, interaction of the particle with its own gravitational perturbation gives rise to an effective 'self-force', which drives the radiative evolution of the orbit, and whose effects can be accounted for order by order in the mass ratio. This review surveys the theory of gravitational self-force in curved spacetime and its application to the astrophysical inspiral problem. We first lay the relevant formal foundation, describing the rigorous derivation of the equation of self-forced motion using matched asymptotic expansions and other ideas. We then review the progress that has been achieved in numerically calculating the self-force and its physical effects in astrophysically realistic inspiral scenarios. We highlight the way in which, nowadays, self-force calculations make a fruitful contact with other approaches to the two-body problem and help inform an accurate universal model of binary black hole inspirals, valid across all mass ratios. We conclude with a summary of the state of the art, open problems and prospects. Our review is aimed at non-specialist readers and is for the most part self-contained and non-technical; only elementary-level acquaintance with general relativity is assumed. Where useful, we draw on analogies with familiar concepts from Newtonian gravity or classical electrodynamics.

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广义相对论中的自力和辐射反应

LIGO-Virgo Collaboration 从双黑洞合并中探测到引力波标志着一个时代的开始，在这个时代，最极端表现的广义相对论动力学可以直接被观察到。未来，计划中的（基于空间的）在毫赫兹波段运行的天文台将探测到来自致密天体螺旋进入位于银河中心的大质量黑洞的复杂引力波信号。这种激励事件是对黑洞几何形状的极其有效的探测，在其最极端的情况下提供了无与伦比的广义相对论精确测试。在过去的 20 年中，这一前景激发了一项计划，以获取具有小质量比的双体系统中强场辐射动力学的准确理论模型。该问题自然适用于基于小质量比中场方程的系统扩展的微扰处理。在领先的顺序中，有一个点状粒子在围绕大黑洞的测地轨道上运动。在随后的顺序中，粒子与其自身引力扰动的相互作用产生了有效的“自力”，它驱动了轨道的辐射演化，其影响可以按质量比依次解释。这篇综述综述了弯曲时空中的引力自力理论及其在天体物理启发问题中的应用。我们首先奠定了相关的形式基础，描述了使用匹配渐近展开和其他思想对自力运动方程的严格推导。然后，我们回顾了在天体物理学现实的灵感场景中数值计算自力及其物理效应方面取得的进展。我们强调了如今自力计算与解决双体问题的其他方法取得卓有成效的联系的方式，并有助于为双黑洞螺旋的准确通用模型提供信息，该模型适用于所有质量比。我们总结了现有技术、未解决的问题和前景。我们的评论针对非专业读者，并且大部分内容是独立的和非技术性的；仅假设对广义相对论有基本的了解。在有用的地方，我们利用牛顿引力或经典电动力学中熟悉的概念进行类比。