The Motion of Point Particles in Curved Spacetime

"The Motion of Point Particles in Curved Spacetime"

Eric Poisson and Adam Pound and Ian Vega

	Abstract
1	Introduction and summary
2	Computing the self-force: a 2010 literature survey
I	General Theory of Bitensors
3	Synge’s world function
4	Coincidence limits
5	Parallel propagator
6	Expansion of bitensors near coincidence
7	van Vleck determinant
II	Coordinate Systems
8	Riemann normal coordinates
9	Fermi normal coordinates
10	Retarded coordinates
11	Transformation between Fermi and retarded coordinates; advanced point
III	Green’s Functions
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
IV	Motion of Point Particles
17	Motion of a scalar charge
18	Motion of an electric charge
19	Motion of a point mass
V	Motion of a Small Body
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
	Appendices
A	Second-order expansions of the Ricci tensor
B	STF multipole decompositions
	References
	Updates
	Figures
	Tables