Tests of General Relativity – Light Deflection  

In General > blue bullet s.a. lensing; phenomenology of gravity; Runge-Lenz Vector.
* Prediction: For a light ray grazing the Sun, using the Schwarzschild metric δφ = 1.75".
* Results: Consistent with γ = 1; 1989, Analysis of radio waves using VLBI in progress, estimate σ(γ) = 0.002; 2005, VLBA results determined γ with an accuracy of 0.0003 using the deflection of four compact radio sources by the solar gravitational field.
* Remark: In general relativity, although particle paths depend on orientation of spin, there is no optical birefringence (> see polarization).
@ Observations: Dyson et al PTRS(20), Dyson Nat(21)feb [May 29, 1919 eclipse]; Fomalont & Sramek PRL(76), Lebach et al PRL(95) [radio waves by the Sun]; news sn(17)jun [starlight deflection by distant star]; Bruns CQG(18) and CQG+ [reenactment of Eddington's measurement with the August 2017 eclipse].
@ Theory, in Schwarzschild spacetime: Lerner AJP(97)dec; Iyer & Petters GRG(07) [analytical perturbation framework]; Pérez & Lamine EJP(18)-a1806 [historical]; Poutanen A&A(20)-a1909 [accurate analytic formula].
@ Theory, in general: Palatini MSAI(23)-a1608; Richter & Matzner ASS(81), PRD(82), PRD(82) [rotating star]; Bruckman & Esteban AJP(93)aug; Dodelson & Wiegert ap/97 [by vector perturbations]; Gerard & Pireaux gq/99; Díaz-Miguel PRD(04) [fall in uniform g field]; Magnan a0712 [complete derivation]; Bhadra a1007 [source and observer not at infinity, weak-deflection limit]; Mak et al AHEP(18)-a1805 [Laplace-Adomian decomposition method]; Ono & Asada Univ-a1906 [finite-distance source and observer]; Arakida a2006 [definition of deflection angle].
@ Beyond linear order: Bodenner & Will AJP(03)aug [to second order]; Brügmann PRD(05)gq [post-linear order]; Hioe PLA(09) [exact expression]; Linet & Teyssandier PRD(16)-a1511 [time transfer functions, unified description of Shapiro and lensing effects].
@ And the equivalence principle: Ferraro AJP(03)feb-gq/02; Díaz-Miguel a0809.
@ Related topics: Mohanty & Prasanna ap/95 [no birefringence]; Fomalont et al IAU(10)-a0912; Unnikrishnan & Gillies IJMPD(09) [classical, quantum, and exotic light]; Li & Chang PRD(10) [quantum gravity effects]; > s.a. history of relativistic physics [1919 eclipse expedition].

By Different Objects / In Other Theories of Gravity > s.a. brans-dicke phenomenology; cosmic-string phenomenology; torsion phenomenology.
@ In Schwarzschild-de Sitter / Kottler spacetime: Islam PLA(83); Lake PRD(02); Rindler & Ishak PRD(07)-a0709 [non-vanishing effect]; Gibbons et al CQG(08)-a0808; Miraghaei & Nouri-Zonoz GRG(10)-a0810 [Newtonian limit]; Bhadra et al PRD(10)-a1007; Arakida & Kasai PRD(12)-a1110; Lebedev & Lake a1308, a1609; Hammad MPLA(13)-a1309; Butcher PRD(16)-a1602; Faraoni & Lapierre-Leonard PRD(17)-a1608 [using the Hawking quasilocal mass, and varying cosmological acceleration]; Arakida GRG(18)-a1708 [definition of the total deflection angle]; Takizawa et al PRD(20)-a2001.
@ With cosmological constant, other metrics: Freire et al GRG(01)gq/02 [with a conical defect].
@ By planets: Kopeikin ap/03 [Jupiter]; Crosta & Mignard CQG(06)ap/05 [and Gaia mission]; Kopeikin & Makarov PRD(07)gq/06 [planetary multipoles]; Malkin et al SSR(09)-a0907 [radio sources]; Fomalont & Kopeikin IAU(07)-a0912 [VLBA results].
@ Kerr metric: Iorio NCB(03)gq/02; Kraniotis CQG(05)gq [and Kerr-AdS]; Edery & Godin GRG(06) [second-order, equatorial]; Iyer & Hansen PRD(09) [equatorial]; Iyer a1810 [asymmetry from frame dragging].
@ Other isolated-object metrics: Ruggiero et al IJMPD(06) [rotating sources, and quadrupole moments]; Sultana PRD(13) [Kerr-de Sitter]; Hu et al AHEP(14)-a1312 [spherically symmetric spacetime, with cosmological constant]; Kraniotis GRG(14)-a1401 [Kerr-Newman and Kerr-Newman-AdS]; Ahmadi & Sedaghatmanesh a1501 [binary system]; Aghili et al GRG(17)-a1408, Piattella PRD-a1508, Univ(16)-a1609 [McVittie metric]; Ono et al PRD(18)-a1806 [rotating wormhole]; news cosmos(18)jun [galaxy ESO 325-G004, 450 Mly away]; Hsiao et al PRD(20)-a1910 [Kerr-Newman black holes].
@ In Weyl gravity: Edery & Paranjape PRD(98)ap/97 [and delay]; Pireaux CQG(04), CQG(04)gq; Cattani et al PRD(13).
@ Related topics: Durrer PRL(94) [in perturbed FLRW spacetime]; Özer & Delice CQG(18)-a1708 [modified gravity with a cosmological term].
@ Quantum-gravity motivated: Tso & Bailey PRD(11)-a1108 [with Lorentz symmetry violation]; Bjerrum-Bohr et al PRL(15)-a1410 [in quantum gravity, one-loop gravitational amplitude]; Xu & Yang JMP(18)-a1709 [higher-order theories].

Examples, Observations, Missions
* LATOR: A proposed mission that would send two laser-transmitter spacecraft behind the Sun to measure the relative gravitational light bending of their signals using a hundred-meter-baseline optical interferometer, to be constructed on the ISS; Should allow a simultaneous determination of the orbit parameters of the spacecraft and of γ with an uncertainty of 2.4 × 10−9, a 6 × 10−9 determination of the solar quadrupole moment J2, and the first measurement of the second-order post-PPN parameter δ to an accuracy of about 10−3.
@ LATOR mission: Turyshev et al CQG(04)gq/03-conf, NPPS(04)gq, ASR(07)gq/04-conf, IJMPD(04)gq-conf, ESA-gq/05, in(06)gq; Plowman & Hellings CQG(06)gq/05; Turyshev & Shao IJMPD(07)gq-proc.
@ Related topics: Zschocke & Klioner a1007 [simplification, for Gaia astrometry mission]; news pt(17)jun [weighing white dwarf Stein 2051 B with light]; Bruns CQG(18)-a1802 [analysis of observations during the 2017-08-21 eclipse].

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