Motion of Relativistic Gravitating Bodies

In General > s.a. gravitational chaos and phenomenology [2-body, etc]; tests of general relativity with orbits.
* Idea: It can be shown that a material object moves along a geodesic in a suitable small-size and small-mass limit; The first corrective effect is that orbits of radiating particles decay from energy loss (has been observed for the binary pulsar).
@ Small size limit: Ehlers & Geroch AP(04)gq/03; Futamase et al PRD(08)-a0811 [small charged black hole].
@ Radiation reaction, Kerr: Ori PLA(95)gq, PRD(97) [Carter invariants]; Mino et al PRD(97); Hughes PRD(00)gq/99, PRD(01)gq; Glampedakis & Kennefick PRD(02)gq, et al PRD(02) [inspiral]; Sago et al PTP(06)gq/05 [evolution of orbit]; > s.a. self-force.
@ Effective 1-body approach: Buonanno & Damour PRD(99); Fiziev & Todorov PRD(01)gq/00.
@ In alternative theories of gravity: Esposito-Farese a0905-ln.

Two-Body Problem > s.a. black-hole thermodynamics; chaos for gravitating bodies; classical systems.
* Idea: As in Newtonian dynamics, can be expressed as a 1-body problem with reduced mass in a fixed potential.
* Modeling: The stationary ones are modeled in general relativity as vacuum or perfect fluid spacetimes with a helical Killing vector field k^a, the corotating generator of time translations; Such systems are not asymptotically flat, but have asymptotic behavior corresponding to equal amounts of ingoing and outgoing radiation.
@ Compact binaries: Portegies Zwart & McMillan ap/99-in [merger rates]; Postnov & Prokhorov ap/99-in; Baumgarte PRD(00)gq [circular orbits]; Gourgoulhon et al PRD(02)gq/01 [spacetime approach]; Alvi PRD(01)gq [E and L in inspiral]; Hartl & Buonanno PRD(05)gq/04 [precessing, PN]; Königsdörffer & Gopakumar PRD(05)gq [eccentric spinning compact binaries, PN]; Futamase & Itoh LRR(07); Damour a0704-ln.
@ 1-body approach: Buonanno & Damour PRD(99)gq/98; Fiziev & Todorov PRD(01).
@ Full 2-body problem: Laguna PRD(99)gq; Damour in(87), et al PRD(00)gq [ADM]; Damour PRD(01)gq [spinning black holes]; Blanchet CRAS-gq/01; Jetzer & Sereno PRD(06)ap [with cosmological constant]; Steinhoff et al PRD(08)-a0809, Hergt & Schäfer PRD(08)-a0809 [spin-spin interaction].

Post-Newtonian Expansion > s.a. classical particles; gravitational collapse; self-force.
@ General references: Blanchet a0907-ln.
@ 1PN: Itoh et al PRD(00)gq/99 [strong field]; Racine & Flanagan PRD(05) [arbitrarily structured bodies].
@ 2PN: Gergely PRD(00)gq [evolution of spinning binaries].
@ 2.5PN: Kidder et al PRD(93); Tagoshi et al PRD(01)gq/00 [spinning]; Itoh et al PRD(01)gq.
@ 3PN: Damour et al PRD(00)gq/99 [invariants]; Blanchet & Faye PLA(00)gq, PRD(01)gq/00; Damour et al PRD(00)gq [last stable orbit], PRD(01)gq/00 [approaches]; Jaranowski & Schäfer AdP(00)gq-in; Porto & Rothstein PRL(06)gq, gq/07-in [spin-spin interaction].
@ 3.5PN: Blanchet et al PRD(02)gq/01 [inspiral]; Pati & Will PRD(02)gq [radiation reaction].
@ With radiation damping and radiation reaction: Burko PRD(03)gq/02 [in Schwarzschild spacetime].
@ Related topics: Rasio ap/99-in [final state]; Arminjon NCB(01)gq [weak field]; Blanchet in(01)gq/02 [accuracy of approximation]; Iorio ASS(07)gq/04 [mean anomaly advance]; Porto & Sturani gq/07-in [and constraints on couplings].

Other Topics and Backgrounds
@ Three-body problem: Imai et al PRL(07)gq [choreographic solution]; Loustó & Nakano CQG(08)-a0710 [post-Newtonian].
> Related topics: see Flyby Anomalies; kaluza-klein theory; test bodies [extended object corrections, semiclassical corrections].

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