Living Reviews in Relativity

"The Motion of Point Particles in Curved Spacetime"
by
Eric Poisson and Adam Pound and Ian Vega  

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Abstract
1 Introduction and summary
2 Computing the self-force: a 2010 literature survey
3 Synge’s world function
4 Coincidence limits
5 Parallel propagator
6 Expansion of bitensors near coincidence
7 van Vleck determinant
8 Riemann normal coordinates
9 Fermi normal coordinates
10 Retarded coordinates
11 Transformation between Fermi and retarded coordinates; advanced point
12 Scalar Green’s functions in flat spacetime
13 Distributions in curved spacetime
14 Scalar Green’s functions in curved spacetime
15 Electromagnetic Green’s functions
16 Gravitational Green’s functions
17 Motion of a scalar charge
18 Motion of an electric charge
19 Motion of a point mass
20 Point-particle limits and matched asymptotic expansions
21 Self-consistent expansion
22 General expansion in the buffer region
23 Global solution in the external spacetime
24 Concluding remarks
25 Acknowledgments
A Second-order expansions of the Ricci tensor
B STF multipole decompositions
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