Motion of Small Objects in Curved Spacetimes: An Introduction to Gravitational Self-Force
Motion of Small Objects in Curved Spacetimes: An Introduction to Gravitational Self-Force
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弯曲时空中小物体的运动：引力自力简介
DOI：
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Pound
中科院分区：
文献类型：
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作者：
A. Pound
近年来，在微扰理论中，已经发展出了描述小型致密物体通过真空背景的任意阶运动的渐近近似方案。该计划是基于严格的方法匹配渐近展开，占对象的有限大小，不需要“正规化”的发散量，并有效的强场和相对论速度。到耦合的对象的多极矩的外部背景曲率，这些计划已经建立，至少通过二阶微扰理论，对象的运动满足广义等效原理：它移动的测地线的一定光滑度规满足真空爱因斯坦方程。我描述了这个结果的基础，特别是专注于如何在微扰理论中表示一个小物体的运动的基本概念。扰动运动的三种常见表示是（i）“Gralla-Wald”描述，即与参考测地线的微小偏差，（ii）“自洽”描述，即服从自加速运动方程的世界线，以及（iii）“密切测地线”描述，它利用了（i）和（ii）。由于广义相对论中的坐标自由，微扰论中任何运动的坐标描述都与理论的规范自由密切相关。我描述的爱因斯坦方程的渐近解适应于每一个运动的三种表示，我讨论的规范自由度与每个。最后，我讨论了如何规范的自由度必须在长期动态的背景下完善。
In recent years, asymptotic approximation schemes have been developed to describe the motion of a small compact object through a vacuum background to any order in perturbation theory. The schemes are based on rigorous methods of matched asymptotic expansions, which account for the object’s finite size, require no “regularization” of divergent quantities, and are valid for strong fields and relativistic speeds. Up to couplings of the object’s multipole moments to the external background curvature, these schemes have established that at least through second order in perturbation theory, the object’s motion satisfies a generalized equivalence principle: it moves on a geodesic of a certain smooth metric satisfying the vacuum Einstein equation. I describe the foundations of this result, particularly focusing on the fundamental notion of how a small object’s motion is represented in perturbation theory. The three common representations of perturbed motion are (i) the “Gralla-Wald” description in terms of small deviations from a reference geodesic, (ii) the “self-consistent” description in terms of a worldline that obeys a self-accelerated equation of motion, and (iii) the “osculating geodesics” description, which utilizes both (i) and (ii). Because of the coordinate freedom in general relativity, any coordinate desscription of motion in perturbation theory is intimately related to the theory’s gauge freedom. I describe asymptotic solutions of the Einstein equations adapted to each of the three representations of motion, and I discuss the gauge freedom associated with each. I conclude with a discussion of how gauge freedom must be refined in the context of long-term dynamics.
影响因子：
5
作者：
Niels Warburton;S. Akçay;L. Barack;J. Gair;N. Sago
通讯作者：
Niels Warburton;S. Akçay;L. Barack;J. Gair;N. Sago