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 regular field that is fully responsible for the selfforce. 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 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 (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.
 Publication:

Living Reviews in Relativity
 Pub Date:
 September 2011
 DOI:
 10.12942/lrr20117
 arXiv:
 arXiv:1102.0529
 Bibcode:
 2011LRR....14....7P
 Keywords:

 electromagnetic field;
 point particles;
 equations of motion;
 self force;
 radiation reaction;
 scalar field;
 curved spacetime;
 gravitation;
 General Relativity and Quantum Cosmology
 EPrint:
 162 pages. Major update of the 2004 version (arXiv:grqc/0306052) initially published in Living Reviews in Relativity. This version contains a thorough literature review (as of 2010) and a lot of new material. v3 reflects referee comments