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arXiv 1005.0611physics.hist-phastro-ph.COastro-ph.HEgr-qc
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自由降落与自力:历史的视角

Free fall and self-force: an historical perspective

Alessandro Spallicci

摘要:

自由降落在物理学史上留下了最伟大的印记,比萨斜塔,剑桥苹果树和爱因斯坦电梯。由超大质量黑洞捕获恒星所提供的前景是值得珍惜的,因为对坠落恒星运动的研究将在理解强场体系中的引力方面向前迈出一大步。在对古代自由降落的概念和牛顿物理学中引力质量的行为进行说明之后,本章讨论了上个世纪关于史瓦西黑洞排斥力的争论,并提到了视界处粒子下落速度的问题。此外,黑洞扰动和数值方法,铺平了道路,引入的自作用力和其他反作用相关的方法。扰动对下落粒子运动的影响通过尾部、扰动的后向散射部分或通过辐射格林函数来计算。在前一种方法中,自作用力作用在背景测地线上;在后一种方法中,测地线被认为是在总场(背景加扰动)中。正则化技术(模和和Riemann-Hurwitz $z$函数)的干预,以消除来自粒子的无穷小尺寸的发散。一个帐户上的最先进的,包括在这个最经典的问题,连同一个角度,包括未来的空间引力波干涉测量和迎面粒子物理实验中获得的最后结果。由于自由降落显然是非绝热的,因此需要最复杂的技术来研究运动的演变。在这种情况下,自洽的方法,通过该方法的背景测地线是不断校正的内力贡献,检查的潜力。

英文摘要:

Free fall has signed the greatest markings in the history of physics through the leaning Pisa tower, the Cambridge apple tree and the Einstein lift. The perspectives offered by the capture of stars by supermassive black holes are to be cherished, because the study of the motion of falling stars will constitute a giant step forward in the understanding of gravitation in the regime of strong field. After an account on the perception of free fall in ancient times and on the behaviour of a gravitating mass in Newtonian physics, this chapter deals with last century debate on the repulsion for a Schwarzschild black hole and mentions the issue of an infalling particle velocity at the horizon. Further, black hole perturbations and numerical methods are presented, paving the way to the introduction of the self-force and other back-action related methods. The impact of the perturbations on the motion of the falling particle is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic; in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisation techniques (mode-sum and Riemann-Hurwitz $z$ function) intervene to cancel divergencies coming from the infinitesimal size of the particle. An account is given on the state of the art, including the last results obtained in this most classical problem, together with a perspective encompassing future space gravitational wave interferometry and head-on particle physics experiments. As free fall is patently non-adiabatic, it requires the most sophisticated techniques for studying the evolution of the motion. In this scenario, the potential of the self-consistent approach, by means of which the background geodesic is continuously corrected by the self-force contribution, is examined.

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