Gravitomagnetism  

In General > s.a. duality; formulations of canonical general relativity; newtonian gravity; stress-energy pseudotensor.
* Idea: Originally, a prerelativistic theory of gravity proposed in 1893 by Oliver Heaviside, based on an analogy between Maxwell's theory of electromagnetism and gravity; It is a flat-space, linear theory with no self-interaction, but the retardation of the field due to the speed of light is taken into account; In the current view, it is a special-relativistic theory that arises in the slow-motion, weak field approximation of general relativity.
* Field equations: The analogs of Maxwell's equations are (H = constant introduced by Heaviside, such that (G/H)1/2 = c)

∇ · g = –4πG ρ ,    ∇ × g = –∂h/∂t ,    ∇ · h = 0 ,    ∇ × h = –4πH ρ v + (H/G) ∂g/∂t .

@ Reviews: Jantzen et al in(96)gq/01; Bini & Jantzen gq/00-proc [references], NCB(00) [rev]; Ruggiero & Tartaglia NCB(02)gq; Mashhoon in(07)gq/03 [and Larmor theorem]; Schäfer GRG(04)gq-in [rev]; Iorio ed-06; Bakopoulos a1610-MS.
@ General references: Heaviside Electr(1893); in Heaviside 1894; Thirring ZP(18); Bedford & Krumm AJP(85)sep; Wheeler IJMPA(88) [conceptual]; Thorne in(88); Harris AJP(91)may [slow motion, weak field equations]; & Schutz; Maartens & Bassett CQG(98)gq/97 [general formalism]; Clark & Tucker CQG(00)gq [perturbative]; Pascual-Sánchez NCB(00)gq [harmonic gauge]; Mashhoon gq/00-proc; Tartaglia & Ruggiero EJP(04)gq/03 [vs electromagnetism]; Wu CTP(05)gq [in gauge theory of gravity]; Maartens GRG(08) [non-linear]; Malekolkalami & Farhoudi MPLA(09)gq/06; Li a1012 [beyond linear order]; Costa & Natário GRG(14)-a1207 [analogies with electromagnetism]; Nouri-Zonoz & Parvizi GRG(16)-a1406 [Papapetrou field]; Costa et al a1603 [intrinsic/extrinsic gravitomagnetism and curvature scalar invariants]; > s.a. riemann tensor [differential-geometric].
@ Quantum theory: Santos & Khanna IJMPA(16)-a1605 [at finite temperature].

Effects, Phenomenology > s.a. maxwell fields in curved spacetime.
* Idea: Gravitomagnetic fields arise from moving matter, like magnetic fields from moving charges, or from distributions of gravitomagnetic monopoles, if they exist (this requires torsion); They do not arise in scalar gravity.
* Clock effect: A deviation from Kepler's third law for a particle in orbit around a (slowly) spinning body, such as a typical planet or star, in the weak-field and slow-motion approximation of general relativity; i.e., a change in the period of revolution of clocks; > s.a. Wikipedia page.
* Other examples: Precession of planetary orbits (not a good test); Precession of gyroscopes; These effects arise in a post-Newtonian, special relativistic treatment of gravitation.
@ General references: Nordtvedt gq/02 [from special relativity + equivalence principle]; Shen gq/03 [and quantum mechanics]; Mashhoon CQG(08)-a0802 [time-varying fields].
@ Observation: Ahmedov & Rakhmatov FP(03)gq [in electromagnetic systems]; Kopeikin IJMPD(06)gq/05 [based on PPN expansion]; Ciufolini a0704 [lunar laser ranging and satellites].
@ Clock effect: Mashhoon et al AdP(99)gq/98, LNP(01)gq/99, PLA(01)gq; Bonnor & Steadman CQG(99); Semerák CQG(99) [extremely accelerated observers]; Tartaglia GRG(00)gq; Lichtenegger et al ASR(00), ASR-gq/01; Bini et al CQG(01)gq/00; Bini & Jantzen gq/01-in; Iorio CQG(01)gq/00, et al CQG(02)gq/01, Tartaglia & Ruggiero gq/01 [neutron interferometry]; Lichtenegger et al AdP(06)gq/02-conf; Faruque PLA(04) [spinning particle in Kerr]; Iorio & Lichtenegger CQG(05) [Earth space-based]; Hackmann & Lämmerzahl PRD(14)-a1406 [generalized]; Faruque et al a1502 [in quantum mechanics]; > s.a. tests of general relativity.
@ On quantum systems: Camacho IJMPD(01)gq/00 [spin-1/2 systems]; Adler & Chen PRD(10)-a0912 [spin-0 particle in electromagnetic + weak gravitational field].
@ Extrinsic gravitomagnetism: Kopeikin & Fomalont GRG(07)gq/05, Kopeikin IJMPD(06) [and light deflection].
@ Other effects: Pascual-Sánchez gq/99-in; de Matos & Tajmar IJP(01)gq/00 [gravitomagnetic Barnett effect]; Tartaglia & Ruggiero gq/01 [rotating mass and light]; Flanders & Japaridze IJTP(02)gq/01 [interaction between moving objects]; Mashhoon IJMPD(05)ap [critical speed]; Mitskievich & López Benítez a0707-MGXI [Zeeman-type]; Bini et al CQG(08)-a0803 [gravitational induction]; Chicone & Mashhoon PRD(11)-a1005 [and astrophysical jets], PLA(11) [gravitomagnetic accelerators]; Ruggiero IJMPD(15)-a1502 [effects of massive rings], ASS(16)-a1507 [gravitomagnetic fields of rotating rings]; Cashen et al PRD(17)-a1610 [gravitomagnetic dynamical friction].
> And tests of general relativity: see gravitational phenomenology; tests with orbits [frame dragging, geodetic precession] and with light.
> Other effects: see gases [ultracold boson gases]; Tajmar Effect; Thomas Precession.

Related Topics
@ Tidal tensor approach: Costa & Herdeiro IAU(09)-a0912 [limitations of electromagnetic analogy]; Voicu JNMP(12)-a1111 [geometric version].
@ Specific spacetimes: Bini et al CQG(03)gq [Kerr-Newman-Taub-NUT], PRD(03)gq [Kerr-Taub-NUT]; Kerr et al CQG(03)gq [with cosmological constant]; > s.a. modified kerr solutions [Kerr-de Sitter].
@ In other theories: Nayeri & Reynolds ht/01 [brane effects]; Camacho GRG(02)gq; Barros & Romero IJMPA(05) [Brans-Dicke]; Spaniol & de Andrade IJMPD(10)-a0802 [teleparallel gravity]; Iorio & Ruggiero JCAP(09)-a0810 [f(R) theories]; Bailey PRD(10)-a1005 [Lorentz-violating]; Exirifard JCAP(13)-a1111; Tasseten & Tekin PRD(16)-a1506 [massive gravity]; Madriz & Montes a1703 [scalar-tensor gauge theory of gravity].
@ Related topics: Lynden-Bell & Nouri-Zonoz RMP(98)gq/96 [monopoles]; Shapiro PRL(96) + pn(96)nov [and LIGO]; Maartens et al CQG(02)gq/01 [and holonomy]; Ghose a0905 [and relativistic particles]; Malekolkalami & Farhoudi IJTP(14)-a1311 [and non-commutative geometry].


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