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 smooth 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 (radiative) 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 (Section 2). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Section 3). It continues with a thorough discussion of Green's functions in curved spacetime (Section 4). The review concludes with a detailed derivation of each of the three equations of motion (Section 5).

中文翻译：

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点粒子在弯曲时空中的运动。

这篇评论与在特定背景时空中的点标量电荷，点电荷和点质量的运动有关。在这三种情况的每种情况下，粒子都会产生一个在波带中充当向外辐射的场，因此会从粒子中除去能量。在附近区域，磁场作用在粒子上并产生自力，该自力可防止粒子在背景时空的测地线上移动。自力既包含保守项也包含耗散项，后者是辐射反应的原因。自力完成的功与粒子辐射掉的能量相匹配。场对粒子的作用由于其奇异性质而难以计算：场在粒子的位置发散。但是可以隔离场的奇异部分，并表明它对粒子没有作用力-它的唯一作用是有助于粒子的惯性。减去后剩下的是一个平滑的场，它完全负责自力。由于该场满足齐次波动方程，因此可以将其视为与粒子相互作用的自由（辐射）场。正是这种相互作用产生了自我力量。这里从零开始开发了在指定的背景时空中导出点标量电荷，点电荷和点质量的运动方程所需的数学工具。这篇综述首先讨论了咬合器的基本理论（第2节）。然后将其应用于方便的坐标系的构建，以绘制粒子的字线的邻域（第3节）。它继续对格林在弯曲时空中的功能进行了详尽的讨论（第4节）。回顾以三个运动方程式的每一个的详细推论结束（第5节）。