Test-Body Orbits in Curved Spacetime  

In General > s.a. force; particle models [including torsion]; orbits of gravitating bodies; self-force [radiation reaction].
* Idea: Pointlike test particles (neutral, spinless) that do not radiate follow geodesics; Charged ones feel, in addition, a Lorentz force; For spinning bodies, their angular momentum is Fermi transported along the geodesic.
* Historical issue: General relativity is the only known theory in which the equation of motion for a particle in the field can be obtained from the field equations; This result was obtained in 1938 by Einstein, Infeld and Hoffmann – it is an important indication of the self-consistency of the theory, and it requires that the field equations be non-linear; The proof uses conservation of the stress-energy tensor applied to dust; This overrides the difficulty of nonexistence of solutions of Einstein's equation with support on a timelike line; Note that one needs for the energy density of matter to be non-negative.
* Corrections: The first corrections to geodesic motion were obtained by Einstein, Infeld & Hoffmann (Lorentz-Droste equations).
* Other modifications: In a theory with torsion, need to distinguish between extremal lines and autoparallels.
@ General references: Brillouin JPR(23)phy/00; Einstein & Grommer SPAW(27); Einstein et al AM(38); Fock JPUSSR(39); Einstein & Infeld AM(40), CJM(49); Infeld & Schild RMP(49); in Infeld RMP(57); Infeld & Plebanski 60; Dixon PTRS(74); Geroch & Jang JMP(75); Nevin GRG(95) [Infeld-Schild theorem], CQG(99); Fernández-Jambrina & Hoenselaers JMP(01) [higher-order corrections]; Boyer AJP(04)aug [unfamiliar trajectories]; Nandi et al EJP(06)gq/05 [from modified Newtonian equations].
@ And gravitoelectromagnetism: Jantzen et al in(87)gq/97.
@ Charged particles: Howard et al PRL(00) + pn(00)mar; Balakin et al CQG(00)gq [in pp-waves and Reissner-Nordström].
@ Spinning particles: Thorne & Hartle PRD(85) [corrections]; Hestenes IJTP(86) [spinor approach]; Karpov JETP(03)gq; > s.a. Weyl Solutions.
@ In modified theories: Mannheim GRG(93) [and dynamical mass]; Dereli & Tucker gq/01 [in Brans-Dicke]; Puetzfeld & Obukhov PRD(08) [with non-minimal matter-curvature coupling]; > s.a. Birkhoff's Theorem, inertia.
@ Modifications: Almeida gq/01 [optical approach]; Accioly & Ragusa CQG(02) [semiclassical]; Dvali et al PRD(03)hp/02 [and Lunar ranging]; Guéron & Letelier ap/03 [interacting geodesics]; Arminjon PRD(05)gq.

In Black Hole Backgrounds > s.a. black-hole phenomenology; chaos in gravitation; geodesics.
* In Schwarzschild: Test bodies can follow stable circular orbits at a radial distance r depending on their angular momentum, but always greater than 6R, where R is the Schwarzschild radius.
* Precession: Non-circular orbits in Schwarzschild do not close; They are only approximately ellipses; With a quadrupole moment, the main contributions are quadr = 6(GM)Qm3/L4, and gr = 6(GM)2m2/L2c2, both positive.
@ General references: Palit et al IJTP(09)-a0808 [stability of circular orbits, phase-space method].
@ Particles in Schwarzschild: in Weinberg 72; Wald 84, pp 140ff; Do-Nhat PLA(98); Dean AJP(99)jan [phase plane analysis]; Mitra gq/99 [radial]; Kerner et al CGQ(01)gq [nearly circular]; Ajith et al PRD(05)gq/04 [post-Newtonian approximants]; Boccaletti et al re GRG(05) [Beltrami's method]; Hall a0807 [exact results].
@ Particles in Kerr spacetime: Hartl PRD(03)gq/02, PRD(03)gq [spinning, (no) chaos]; Teo GRG(03) [photons, closed]; Boccaletti et al re GRG(05) [Beltrami's method]; Rosquist et al a0710 [meaning of Carter's constant]; > s.a. kerr spacetime.
@ Precession: in Weinberg 72; Stump AJP(88)dec, comment Doggett AJP(91)sep; Scales & Cornelius JURP(93).
@ Epicyclic oscillations: Abramowicz & Kluzniak GRG(03)gq/02; Biesiada GRG(03)gq [vs Newtonian].
> Other spacetimes: see gravitational waves; schwarzschild; schwarzschild-de sitter.
> Online resources: see John Walker's page and applet.

Other Effects and Backgrounds > s.a. classical particle models.
* Reverse centrifugal force: The critical distance, within which the effect is seen is (3/2) rS; > s.a. force.
@ Reverse centrifugal force: Allen Nat(90)oct; Abramowicz MNRAS(92), SA(93)mar; Bini et al IJMPD(97)gq/01, IJMPD(97)gq/01; Prasanna MPLA(02) [ADM view]; Jonsson AJP(06)oct-a0708 [intuitive approach].
@ Antigravity: Felber gq/05 [repulsive weak field at high v], gq/05 [propulsion].
@ Periastron precession: Bini et al GRG(05) [Weyl solutions]; > s.a. newtonian orbits.
@ Resonances: Abramowicz et al CQG(02)gq; Rebusco AN(05)ap [compact objects].
@ Swimming in curved spacetime: Blau PT(03)jun; Guerón et al PRD(06)gq/05; > s.a. Extended Objects.
@ Related topics: Rothman et al CQG(01)gq/00 [quantized holonomy]; Bini et al CQG(03) [in colliding plane waves]; Ilhan a0911-MSc [equations of motion in terms of multipoles].

In Cosmological Backgrounds > s.a. chaos in gravitation.
* Issues: Do orbits of planets expand because of the global universal expansion? If so, at what rate? Are there any other local effects of the global expansion?
@ With a cosmological constant: Kerr et al CQG(03)gq [clocks and orbit precession]; > s.a. cosmological constant.
@ And cosmological expansion: Cooperstock et al ApJ(98)ap; Baker ap/99-wd, ap/00/PRD; Bolen et al CQG(01)gq/00 [precession]; Licht gq/01 [no effect on Pioneer]; > s.a. anomalous acceleration, relativistic cosmology [local effects].

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