Test-Body Motion in Curved Spacetime  

In General > s.a. classical particles [including torsion]; force; geodesics; motion of gravitating bodies; self-force [radiation reaction].
* Idea: Pointlike test particles (neutral, spinless) that do not radiate follow timelike geodesics (geodesic hypothesis/principle); 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 non-existence 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, one needs 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 & Plebański 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]; Barone et al JGP(11); Weatherall FP(12)-a1106 [role of energy conditions]; Weatherall FP(12) [energy conditions and the Geroch-Jang theorem]; Tamir SHPMP(12) [the geodesic principle and universality]; Yang CMP(14) [rigorous derivation]; Savickas IJMPD(14) [in terms of Newton's laws within curved geometries]; Weatherall a1810 [new approach based on "tracking"].
@ 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 spacetime].
@ Spinning particles: Thorne & Hartle PRD(85) [corrections]; Hestenes IJTP(86) [spinor approach]; Karpov JETP(03)gq; Hojman & Asenjo a1810 [non-geodesic circular motion]; Keresztes & Mikóczi a1907 [in rotating black-hole spacetimes]; > s.a. Weyl Solutions.
@ Particles with internal structure: Sławianowski & Gołubowska RPMP(10) [curved spaces, analysis based on non-holonomic frames].
@ In other theories: Mannheim GRG(93) [and dynamical mass]; Dereli & Tucker gq/01 [Brans-Dicke theory]; Puetzfeld & Obukhov PRD(08) [with non-minimal matter-curvature coupling]; Gralla PRD(10)-a1002; Weatherall JMP(11)-a1010, SHPMP(11)-a1106 [in Newton-Cartan theory]; Puetzfeld & Obukhov PRD(13)-a1303, PLA(13) [with general non-minimal coupling]; Kahil a1502 [in bimetric gravity]; > s.a. Birkhoff's Theorem; hořava-lifshitz gravity; inertia.
@ In higher dimensions: Dadhich et al PRD(13)-a1308 [Lovelock gravity, but not general relativity, has bound orbits around a static source].
@ 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; > s.a. motion in newtonian gravity [pseudo-Newtonian limit].

In Black Hole Backgrounds > s.a. black-hole phenomenology; Carter Constant; chaos in gravitation; geodesics.
@ General references: Palit et al IJTP(09)-a0808 [stability of circular orbits, phase-space method]; Tejeda & Rosswog a1402 [spherically symmetric spacetimes, generalized Newtonian description]; Bhattacharya et al PRD(15)-a1412 [around static black holes, in Einstein and Lovelock gravity].
@ 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; particles in kerr spacetimes; schwarzschild solution; schwarzschild-de sitter solution.
> Online resources: see John Walker's page and applet.

In Cosmological Backgrounds > s.a. chaotic motion.
* 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].

Other Effects and Backgrounds > s.a. classical particle models; kaluza-klein phenomenology.
* 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]; Dalakishvili a1110 [from the perspective of rigidly rotating observer].
@ Antigravity: Felber gq/05 [repulsive weak field at high v], AIP(06)gq/05 [propulsion].
@ Periastron / perihelion precession: Bini et al GRG(05) [Weyl solutions]; Poveda & Marín a1802 [higher-order corrections]; > s.a. newtonian orbits; schwarzschild-de sitter spacetime.
@ 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]; Iorio NS(10)gq/05 [isotropic mass loss by the central body]; Ilhan MSc(09)-a0911 [equations of motion in terms of multipoles]; Ahmadzadegan et al PRD(14)-a1406 [atoms with internal degrees of freedom as probes]; > s.a. wormhole solutions [Einstein-Rosen bridge].

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