点粒子在弯曲时空中的运动

IF 26.3 2区 物理与天体物理 Q1 PHYSICS, PARTICLES & FIELDS
Eric Poisson, Adam Pound, Ian Vega
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引用次数: 566

摘要

本文讨论了点标量电荷、点电荷和点质量在特定背景时空中的运动。在这三种情况中,粒子产生的场在波区表现为向外辐射,因此从粒子中去除能量。在近区域,场作用于粒子并产生自作用力,阻止粒子在背景时空的测地线上移动。自作用力包含保守项和耗散项,耗散项负责辐射反应。自作用力所做的功与粒子辐射出去的能量相匹配。场对粒子的作用很难计算,因为它的奇异性:场在粒子的位置发散。但是有可能分离出磁场的奇异部分,并证明它对粒子不施加任何力——它唯一的作用是增加粒子的惯性。减法后剩下的是一个规则场,它完全负责自我力。因为这个场满足齐次波动方程,它可以被认为是一个与粒子相互作用的自由场;正是这种相互作用产生了自我力量。推导点标量电荷、点电荷和点质量在特定背景时空中的运动方程所需要的数学工具在这里从零开始发展。回顾首先讨论了位传感器的基本理论(第一部分)。然后将该理论应用于构建方便的坐标系来绘制粒子词线的邻域(第二部分)。接着深入讨论了弯曲时空中的格林函数(第三部分)。回顾给出了三个运动方程中的每个方程的详细推导(第四部分)。因为点质量的概念在广义相对论中是有问题的。回顾总结(第五部分)与运动方程的另一种推导,适用于任意内部结构的小体。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

The Motion of Point Particles in Curved Spacetime

The Motion of Point Particles in Curved Spacetime

This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.

The field’s action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field’s singular part and show that it exerts no force on the particle — its only effect is to contribute to the particle’s inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force.

The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle’s word line (Part II). It continues with a thorough discussion of Green’s functions in curved spacetime (Part III). The review presents a detailed derivation of each of the three equations of motion (Part IV). Because the notion of a point mass is problematic in general relativity, the review concludes (Part V) with an alternative derivation of the equations of motion that applies to a small body of arbitrary internal structure.

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来源期刊
Living Reviews in Relativity
Living Reviews in Relativity 物理-物理:粒子与场物理
CiteScore
69.90
自引率
0.70%
发文量
0
审稿时长
20 weeks
期刊介绍: Living Reviews in Relativity is a peer-reviewed, platinum open-access journal that publishes reviews of research across all areas of relativity. Directed towards the scientific community at or above the graduate-student level, articles are solicited from leading authorities and provide critical assessments of current research. They offer annotated insights into key literature and describe available resources, maintaining an up-to-date suite of high-quality reviews, thus embodying the "living" aspect of the journal's title. Serving as a valuable tool for the scientific community, Living Reviews in Relativity is often the first stop for researchers seeking information on current work in relativity. Written by experts, the reviews cite, explain, and assess the most relevant resources in a given field, evaluating existing work and suggesting areas for further research. Attracting readers from the entire relativity community, the journal is useful for graduate students conducting literature surveys, researchers seeking the latest results in unfamiliar fields, and lecturers in need of information and visual materials for presentations at all levels.
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