Gravitational Lensing  

In General > s.a. aharonov-bohm effect; dark matter.
* 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 can use Fermat's principle.
* Theoretical results: There is always an odd number of images, unless they are formed by a black hole; Has enriched the field of geometrical optics.
* Experimental results: VLA surveys yield few lenses; the universe cannot be closed by masses of 1011–1012 MSun; 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: Look for cosmic strings with the space telescope; dark matter.

In Specific Spacetimes > s.a. observational cosmology; gravitational-wave propagation; tests of general relativity with light.
@ By black holes: Virbhadra & Ellis PRD(00)ap/99 [Schwarzschild]; Eiroa et al PRD(02)gq [Reissner-Nordström]; Vázquez & Esteban NCB(04)gq/03 [Kerr]; Whisker PRD(05)ap/04 [brane world]; Eiroa PRD(06) [Einstein-Born-Infeld]; Konoplya PLB(07) [magnetized]; Sereno PRD(08), PRL(09), Bozza PRD(08)-a0806 [caustics], a0911-GRG [rev].
@ With cosmological constant: Lake PRD(02)gq/01, a0711; Park PRD(08)-a0804; Ishak et al a0810 [Schwarzschild-de Sitter]; Schücker GRG(09); Khriplovich & Pomeransky IJMPD(08).
@ By wormholes: Eiroa et al MPLA(01)gq, Torres et al MPLA(01)gq [chromaticity]; Safonova et al PRD(02)gq/01; Shatskiy AR(04)ap; Tejeiro & Larrañaga gq/05; Nandi et al PRD(06)gq; Kanti Dey & Sen MPLA(08)-a0806; > s.a. wormholes.
@ Other isolated objects: Virbhadra & Ellis PRD(02) [naked singularity]; Palle APS(05)ap [quadrupole potentials]; Amore et al PRD(07) [compact objects].
@ Cosmic strings: de Laix PRD(97), et al PRL(97); Bernardeau & Uzan PRD(01)ap/00, ap/00-in; Shlaer & Tye PRD(05) [and instability of closed timelike curves]; Agol et al PRD(06) [HST candidate excluded]; Gasparini et al MNRAS(08)-a0710; > s.a. tests of general relativity with light [conical defects].
@ Gravitational waves: Mollerach PRD(98)ap/97; Faraoni IJMPD(98), & Gunzig A&A(98)ap [scalar-tensor]; Bisnovatyi-Kogan & Tsupko G&C(08)-a0809.
@ Cosmological models: Wambsganss et al ap/96/ApJ; Kaiser ApJ(98)ap/96; Ghassemi et al PRD(09) [Lemaître-Tolman-Bondi].
@ Inhomogeneous, cumulative: Holz & Wald PRD(98)ap/97, Wald gq/98-in [statistical distribution]; Bergstrom et al A&A-ap/99; Claudel PRS(00)gq [including swiss cheese]; Jain et al PRD(02)ap [brane world]; > s.a. relativistic cosmology [local models].
@ Related topics: Zaldarriaga PRD(00)ap/99 [and cmb]; Safonova et al MPLA(01)ap [violations of energy conditions].

Microlensing > s.a. cosmic strings; dark matter.
* Idea: Gravitational lensing by small objects such as planets; Gives very small image separation (< 1 mas) but brighter images; One tends to find more outer planets than with Doppler shifts or transits, bright star not needed, and one can measure the mass without seeing the planet.
* History: 1936, Paper by Einstein & R W Mandl (Czech engineer who prodded him); 1964, Liebes PP, Refsdal MNRAS; 1986, Paczynski proposed use for dark matter detection; 1998, 1-m telescopes start looking; 1999, Planet around a binary system found with it.
@ Reviews, intros: Paczynski & Wambsganss PW(93); Evans ap/96-in; Gould ap/96-in, ap/00-in; Roulet & Mollerach PRP(97); Mao ap/99-in; Paczynski ap/99-in; Sackett ap/00-in; Evans ap/03-in; Paczynski ap/03 [and future]; Rattenbury MPLA(06) [planetary]; Zakharov ap/06-in; Gould a0803-in; Mao a0811-in.
@ Theory, formalism: Gould ap/00/ApJ; Asada ApJ(02)ap [perturbative]; Petters et al JMP(09)-a0807 [stochastic].
@ Of gravitational waves: Bar-Kana PRD(96)ap [limits on background]; De Paolis et al A&A(01)ap/00.
@ Related topics: Gould ap/96-in [imaging binaries, quasars]; Jetzer HPA(96)ap, ap/97-in [dark matter search]; MACHO collab ap/97-in [data]; Paczynski ap/97/ApJL [SIM plans]; Han et al MNRAS(00)ap/99, ApJ(04)ap/03 [free-floating planets]; Smith et al MNRAS(03)ap/02 [acceleration and parallax effects]; Kuijken et al MNRAS(08)-a0707 [by cosmic strings].

Weak Lensing
* Idea: Gravitational lensing that produces a small distorsion in images of background galaxies; It cannot be recognized as lensing on the basis of a single galaxy image, but one uses the statistical properties of many galaxies in a region of the sky.
@ General references: Bartelmann & Schneider PRP(01); Mellier & van Waerbeke CQG(02)in.
@ In various gravity theories: Acquaviva et al PRD(04)ap, ap/04-in; Song & Doré JCAP(09) [test of general relativity vs f(R) theories]; Hearin & Zentner JCAP(09) [gravity tests and galaxy-formation physics].
@ In cosmology: Massey et al ap/04-in [dark matter and dark energy]; Munshi et al PRP(08), Hoekstra & Jain ARNPS-a0805 [rev]; Hanson et al a0911-GRG [of cmb].

References
@ General: Ohanian AJP(87)may; Blandford et al Sci(89)aug; in Texas XVII(95); Schechter ap/99-in [review]; Blandford PASP(01)ap [future]; Wambsganss SA(01)nov; Perlick LRR(04) [spacetime perspective]; Sauer a0704 [history, Einstein and Nova Geminorum 1912]; Jain NJP(07) [focus issue].
@ Theory: Frittelli & Newman PRD(99)gq/98; Kling et al PRD(00)gq/99 [iterative]; Frittelli et al PRD(00)gq [Schwarzschild], PRD(01)gq/00, PRD(01)gq/00 [image distorsion], PRD(02)gq [non-perturbative]; Kochanek et al ap/00/ApJ [Einstein rings]; Hasse & Perlick GRG(02)gq/01 [and centrifugal force reversal]; Frittelli MNRAS(03)ap [by moving lenses]; Suyama et al PRD(05)ap [wave propagation and thin 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].
@ Intros, reviews: Turner SA(88)jul; Narayan & Bartelmann ap/96; Straumann ap/97; Schneider et al 92; Wambsganss LRR(98)ap; Fluke et al ap/98/MNRAS [new method]; Mollerach & Roulet IJMPA(00)ap/99; Wambsganss ap/00-in, ap/06-in; Kuijken ap/03-ln; Koopmans & Blandford PT(04)jun [and applications]; Falco NJP(05).
@ Of other electromagnetic waves: Lu & Pen a0710/MNRAS [21-cm radiation, diffuse].
@ Of gravitational waves: Wang et al PRL(96); De Paolis et al A&A(02)ap.
@ Used as test of gravity theories: Keeton & Petters PRD(05), PRD(06); Smith a0907/PRD; Schwab et al a0907; Bean a0909 [results disfavor general relativity for 1 < z < 2].
@ And other 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]; > s.a. cosmic microwave background.
@ Related topics: Asada & Kasai PTP(00)ap [lens rotation]; Frutos-Alfaro AJP(01)feb-ap/02 [visualization program]; Ciufolini & Ricci gq/03/PRL [and time delay]; Nemiroff ApJ(05)ap [magnifying gravity]; > s.a. higher-dimensional gravity; philosophy of science; tests of lorentz invariance.

main page – abbreviations – journals – comments – other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 11 nov 2009