Living Reviews in Relativity

"The Motion of Point Particles in Curved Spacetime"
by
Eric Poisson  

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Abstract
1 Introduction and Summary
1.1 Invitation
1.2 Radiation reaction in flat spacetime
1.3 Green’s functions in flat spacetime
1.4 Green’s functions in curved spacetime
1.5 World line and retarded coordinates
1.6 Retarded, singular, and radiative electromagnetic fields of a point electric charge
1.7 Motion of an electric charge in curved spacetime
1.8 Motion of a scalar charge in curved spacetime
1.9 Motion of a point mass, or a black hole, in a background spacetime
1.10 Evaluation of the self-force
1.11 Organization of this review
2 General Theory of Bitensors
2.1 Synge’s world function
2.2 Coincidence limits
2.3 Parallel propagator
2.4 Expansion of bitensors near coincidence
2.5 Van Vleck determinant
3 Coordinate Systems
3.1 Riemann normal coordinates
3.2 Fermi normal coordinates
3.3 Retarded coordinates
3.4 Transformation between Fermi and retarded coordinates; advanced point
4 Green’s Functions
4.1 Scalar Green’s functions in flat spacetime
4.2 Distributions in curved spacetime
4.3 Scalar Green’s functions in curved spacetime
4.4 Electromagnetic Green’s functions
4.5 Gravitational Green’s functions
5 Motion of Point Particles
5.1 Motion of a scalar charge
5.2 Motion of an electric charge
5.3 Motion of a point mass
5.4 Motion of a small black hole
5.5 Concluding remarks
6 Acknowledgments
Open References References
Footnotes
Figures