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).
@ General references: Asada et al 11 [inclusing charge, spin, and gravitational radiation effects].
@ Small-size limit: Ehlers & Geroch AP(04)gq/03; Futamase et al PRD(08)-a0811 [small charged black hole]; Gralla PRD(10)-a1002; Poisson et al LRR(11)-a1102; Gralla & Wald CQG(11) [coordinate freedom]; Gralla PRD(13)-a1303 [mass and charges as explicit surface integrals]; > s.a. test-body motion [geodesics and extended-object corrections, semiclassical corrections].
@ Radiation reaction, Schwarzschild: Warburton et al PRD(12)-a1111 [evolution of inspiral orbits]; Diener et al PRL(12)-a1112 [charged particle, fully self-consistent orbits and waveforms].
@ 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, Sago & Fujita PTEP(15)-a1505 [evolution of orbit]; > s.a. gravitational self-force.
@ In alternative theories of gravity: Esposito-Farèse FTP(11)-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 ka, 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.
@ General references: Damour a1312-fs [rev]; Foffa et al a1612 [effective field theory approach].
@ Spin-orbit coupling: Porto CQG(10); Iorio GRG(12)-a1012 [exact, and spin-spin effects]; Hartung & Steinhoff AdP(11)-a1104 [post-Newtonian spin-orbit Hamiltonian]; Bini & Damour PRD(14)-a1404; Levi & Steinhoff a1506, a1506 [effective field theory approach, up to 4PN order].
@ Compact binaries: Portegies Zwart & McMillan ap/99-conf [merger rates]; Postnov & Prokhorov ap/99-conf; 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; Foffa & Sturani CQG(14) [effective field theory methods].
@ Effective 1-body approach: Buonanno & Damour PRD(99)gq/98; Fiziev & Todorov PRD(01)gq/00; Damour in(14)-a1212 [rev].
@ 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(01)gq; Jetzer & Sereno PRD(06)ap [with cosmological constant]; Steinhoff et al PRD(08)-a0809, Hergt & Schäfer PRD(08)-a0809 [spin-spin interaction]; Kol & Smolkin PRD(09) [dressed-perturbation-theory approach]; Bini et al PRD(15)-a1510 [spin-dependent two-body interactions from gravitational self-force]; > s.a. types of black holes [binaries].

Post-Newtonian Expansion > s.a. classical particles; gravitational collapse; gravitational ; particles in schwarzschild spacetime.
* Applicability: It works best for pairs of objects with values of the mass ratio far from 1, and breaks down when the objects are very close.
@ General references: Blanchet a0907-ln; De Laurentis a1004.
@ 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-proc; Porto & Rothstein PRL(06)gq, gq/07-MG11 [spin-spin interaction].
@ 3.5PN: Blanchet et al PRD(02)gq/01 [inspiral]; Pati & Will PRD(02)gq [radiation reaction].
@ Related topics: Rasio ap/99-conf [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-proc [and constraints on couplings]; Foffa & Sturani PRD(13)-a1206 [at 4PN order, up to quadratic terms in G].

Other Topics and Backgrounds > s.a. dynamics of gravitating bodies.
@ Three-body problem: Imai et al PRL(07)gq [choreographic solution in general relativity]; Loustó & Nakano CQG(08)-a0710 [post-Newtonian].
> Related topics: see Flyby Anomalies; kaluza-klein theory.


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