The Motion of Point Particles in Curved Spacetime
Abstract
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 selfforce that prevents the particle from moving on a geodesic of the background spacetime. The selfforce contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the selfforce 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 selfforce. 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 selfforce. 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).
 Publication:

Living Reviews in Relativity
 Pub Date:
 May 2004
 DOI:
 10.12942/lrr20046
 arXiv:
 arXiv:grqc/0306052
 Bibcode:
 2004LRR.....7....6P
 Keywords:

 Point particles;
 Radiation reaction;
 Self force;
 Equations of motion;
 Curved spacetime;
 Scalar field;
 Electromagnetic field;
 Gravitation;
 Gravitational Waves;
 General Relativity and Quantum Cosmology
 EPrint:
 LaTeX2e, 116 pages, 10 figures. This is the final version, as it will appear in Living Reviews in Relativity