Gravitational Lensing  

In General > s.a. aharonov-bohm effect; dark-matter detection; gravitational light bending.
* Idea: The lens-like effect produced by the deflection of waves (especially light) along different paths.
* Remark: They are not linear lenses, and are not described by Gaussian optics, but one can use Fermat's principle.
* Experimental results: VLA surveys yield few lenses; The universe cannot be closed by masses of \(10^{11}\)–\(10^{12}\; M_\odot\); They allow us to make spectra of distant (z > 2) galaxies, because of amplification (they are like 100-Kpc telescopes); Many double images of galaxies (some with opposite parity) have been seen; The first complete Einstein ring has been seen, and the (extended) source object reconstructed.
* Future: 2000s, Look for cosmic strings with the space telescope; Find planets; Measure dark-matter distributions.
> Online resources: see Simulating eXtreme Spacetimes page.

Theory > s.a. optics [optical geometry]; lensing in specific spacetimes [including cosmological constant].
* Results: There is always an odd number of images, unless they are formed by a black hole; Lensing has enriched the field of geometrical optics.
@ General references: Frittelli & Newman PRD(99)gq/98; Kling et al PRD(00)gq/99 [iterative]; Frittelli et al PRD(01)gq/00, PRD(01)gq/00 [image distorsion], PRD(02)gq [non-perturbative]; Kochanek et al ApJ(01)ap/00 [Einstein rings]; Frittelli MNRAS(03)ap [by moving lenses]; Amore & Arceo PRD(06), Amore et al PRD(06) [analytical expressions]; Werner JMP(07)mp [topological invariants, fixed-point theorem]; Bozza PRD(08)-a0807 [approximate equations]; Petters & Werner GRG(10)-a0912 [multiple images and magnification]; Heavens a1109-ln [and tests of general relativity]; Aazami & Werner JGP-a1507, Werner a1507-MG14 [geometric definition of magnification]; Harte GRG(19)-a1808 [beyond geometric optics]; Normann & Clarkson GRG(20)-a1904 [recursion relations].
@ And MOND: Soussa & Woodard PLB(04)ap/03 [problem]; Zhao et al MNRAS(06)ap/05; Mavromatos et al PRD(09)-a0901; Ferreras et al PRD(09)-a0907 [and rotation curves]; Ferreras et al PRD(12)-a1205 [extended survey]; Milgrom PRL(13)-a1305; > s.a. MOND.
@ And other gravity theories: Sereno PRD(03)ap [metric theories]; Schimd et al PRD(05)ap/04 [scalar-tensor including quintessence]; Capozziello et al PRD(06)ap [4th-order gravity]; Zhao ap/06-ln, Chen JCAP(08)-a0712 [TeVeS]; Ruggiero GRG(09)-a0712 [f(R), Palatini approach]; Schmidt PRD(08)-a0805 [f(R) gravity, DGP, TeVeS]; Nzioki et al PRD(11)-a1002 [f(R) gravity]; Martinelli et al PRD(11) [satellite mission tests]; Werner a1904-MG15 [area-metric spacetimes]; > s.a. cosmic microwave background; hořava gravity; Modified Gravity.
@ Use of lensing as test of gravity theories: Knox et al PRD(06)ap/05 [lensing, dark energy and new gravity]; Keeton & Petters PRD(05), PRD(06); Smith a0907/PRD; Schwab et al ApJ(09)-a0907; Bean a0909-wd [results disfavor general relativity for 1 < z < 2]; Bean & Tangmatitham PRD(10)-a1002; Liu & Prokopec PLB(17)-a1612 [Verlinde's emergent gravity]; > s.a. cosmology in higher-order theories.
@ Related topics: Hasse & Perlick GRG(02)gq/01 [and centrifugal force reversal]; Suyama et al PRD(05)ap [wave propagation and thin lenses].

References > s.a. types of lensing [microlensing, weak lensing].
@ General: Ohanian AJP(87)may [Schwarzschild black hole]; Blandford et al Sci(89)aug; in Böhringer et al 95; Schechter ap/99-proc [review]; Blandford PASP(01)ap [future]; Wambsganss SA(01)nov; Perlick LRR(04)-a1010 [spacetime perspective]; Jain NJP(07) [focus issue]; Treu et al AJP(12)sep-a1206 [RL]; Huwe & Field TPT(15)#5 [undergraduate lab]; Sauer & Schütz EJP(19)-a1905 [pedagogical].
@ History: Valls-Gabaud AIP(06)-a1206; Sauer AHES(08)-a0704 [history, Einstein and Nova Geminorum 1912]; Will CQG(15)-a1409 [1919 measurement of the deflection of light, etc]; Treu & Ellis a1412-in [rev].
@ Observation: news pw(13)oct [most distant lens seen 9.4 Gly away]; Udalski et al AA-a1504 [OGLE-IV survey].
@ Intros, reviews: Turner SA(88)jul; Narayan & Bartelmann ap/96; Straumann ap/97; Schneider et al 92; Wambsganss LRR(98)ap; Fluke et al MNRAS(99)ap/98 [new method]; Mollerach & Roulet IJMPA(00)ap/99; Wambsganss ap/00-IAU, in(06)ap; Kuijken ASP-ap/03; Koopmans & Blandford PT(04)jun [and applications]; Falco NJP(05); Schneider et al ed-06; Jetzer et al ed-GRG(10)#9; Bartelmann CQG(10)-a1010; Dodelson 17.
@ Time delay: Ciufolini & Ricci gq/03/PRL; Gürkan et al a1011-conf [efficient measurement]; Linder PRD(11) [and cosmological complementarity]; Takahashi ApJ(17)-a1605 [time differences between gravitational and electromagnetic waves]; Piattella & Giani PRD(17)-a1703 [and redshift drift].
@ Of the cmb: Das et al PRL(11), Sherwin et al PRL(11) + Boughn Phy(11) [and dark energy]; Jenkins et al PLB(14)-a1403 [Feynman diagram approach].
@ Of other electromagnetic waves: Lu & Pen MNRAS(08)-a0710 [21-cm radiation, diffuse].
@ Of gravitational waves: Wang et al PRL(96); De Paolis et al A&A(02)ap; Sereno et al PRD(10) [merging of supermassive black holes and LISA]; Christian et al PRD(18)-a1802 [and detection]; Hannuksela et al ApJL(19)-a1901 [in LIGO-Virgo binary black hole events].
@ Related topics: Asada & Kasai PTP(00)ap [lens rotation]; Frutos-Alfaro AJP(01)feb-ap/02 [visualization program]; Courbin & Minniti ed-02 [and astrophysics]; Nemiroff ApJ(05)ap [magnifying gravity]; Zhang et al PRL(07) [relationship between lensing and matter overdensity]; Tippett PRD(11)-a1109 [and cloaking]; > s.a. higher-dimensional gravity; philosophy of science; quantum equivalence principle and tests of the equivalence principle; tests of lorentz invariance.

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