Title 
The Motion of Point Particles in Curved Spacetime


Published in 
Living Reviews in Relativity, May 2004

DOI  10.12942/lrr20046 
Pubmed ID  
Authors 
Eric Poisson 
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). 
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South Africa  4  400% 
Brazil  3  300% 
Other  38  3800% 
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Student > Ph. D. Student  460  46000% 
Researcher  207  20700% 
Student > Master  167  16700% 
Unspecified  87  8700% 
Student > Doctoral Student  76  7600% 
Other  257  25700% 
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Engineering  253  25300% 
Unspecified  187  18700% 
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Other  234  23400% 