2 History of Gravitational Lensing

The first written account of the deflection of light by gravity appeared in the “Berliner Astronomisches Jahrbuch auf das Jahr 1804” in an article entitled: “Über die Ablenkung eines Lichtstrahls von seiner geradlinigen Bewegung, durch die Attraktion eines Weltkörpers, an welchem er nahe vorbeigeht” (“On the Deflection of a Light Ray from its Straight Motion due to the Attraction of a World Body which it Passes Closely”) [175]. Johann Soldner – a German geodesist, mathematician and astronomer then working at the Berlin Observatory – explored this effect and inferred that a light ray close to the solar limb would be deflected by an angle &tidle;α = 0.84 arcsec. It is very interesting to read how carefully and cautiously he investigated this idea and its consequences on practical astronomy.

In the year 1911 – more than a century later – Albert Einstein [50] directly addressed the influence of gravity on light (“Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes” (“On the Influence of Gravity on the Propagation of Light”). At this time, the General Theory of Relativity was not fully developed. This is the reason why Einstein obtained – unaware of the earlier result – the same value for the deflection angle as Soldner had calculated with Newtonian physics. In this paper, Einstein found &tidle;α = 2G M ∕c2R = 0.83 arcsec ⊙ ⊙ for the deflection angle of a ray grazing the sun (here M ⊙ and R ⊙ are the mass and the radius of the sun, c and G are the velocity of light and the gravitational constant, respectively). Einstein emphasized his wish that astronomers investigate this question (“Es wäre dringend zu wünschen, daß sich Astronomen der hier aufgerollten Frage annähmen, auch wenn die im vorigen gegebenen Überlegungen ungenügend fundiert oder gar abenteuerlich erscheinen sollten.” (“It would be very desirable that astronomers address the question unrolled here, even if the considerations should seem to be insufficiently founded or entirely speculative.”) Recently it was discovered that Einstein had derived the lens equation, the possibility of a double image and the magnifications of the images in a notebook in the year 1912 [153Jump To The Next Citation Point]. In 1913 Einstein even contacted the director of the Mt. Wilson Observatory, George Ellery Hale, and asked him whether it would be possible to measure positions of stars near the sun during the day in order to establish the deflection effect of the sun.

See [51] to view a facsimile of a letter Einstein wrote to G.E. Hale on October 14, 1913. In the letter, Einstein asked Hale whether it would be possible to determine the light deflection at the solar limb during the day. However, there was a “wrong” value of the deflection angle in a sketch Einstein included in the letter.

There actually were plans to test Einstein’s wrong prediction of the deflection angle during a solar eclipse in 1914 on the Russian Crimea peninsula. However, when the observers were already in Russia, World War I broke out and they were captured by Russian soldiers [32]. So, fortunately for Einstein, the measurement of the deflection angle at the solar limb had to be postponed for a few years.

With the completion of the General Theory of Relativity, Einstein was the first to derive the correct deflection angle &tidle;α of a light ray passing at a distance r from an object of mass M as

&tidle;α = 4GM---1, (1 ) c2 r
where G is the constant of gravity and c is the velocity of light. The additional factor of two (compared to the “Newtonian” value) reflects the spatial curvature (which is missed if photons are just treated as particles). With the solar values for radius and mass Einstein obtained [5253]:
&tidle;α = 4G-M-⊙--1--= 1.74 arcsec. (2 ) ⊙ c2 R ⊙
It is common wisdom now that the determination of this value to within 20% during the solar eclipse in 1919 by Arthur Eddington and his group was the second observational confirmation of General Relativity [47] and the basis of Einstein’s huge popularity starting in the 1920s. (The first one had been the explanation of Mercury’s perihelion shift.) Recently, the value predicted by Einstein was confirmed to an accuracy better than 0.02% [107].

In the following decades, light deflection or gravitational lensing was only very rarely the topic of a research paper: In 1924, Chwolson [39Jump To The Next Citation Point] mentioned the idea of a “fictitous double star” and the mirror-reversed nature of the secondary image. He also mentioned the symmetric case of star exactly behind star, resulting in a circular image. Einstein also reported in 1936 about the appearance of a “luminous circle” for perfect alignment between source and lens [54Jump To The Next Citation Point], and of two magnified images for slightly displaced positions1. Today such a lens configuration is called “Einstein-ring”, although more correctly it should be called “Chwolson-ring”. Influenced by Einstein, Fritz Zwicky [210211] pointed out in 1937 that galaxies (“extragalactic nebulae”) are much more likely to be gravitationally lensed than stars and that one can use the gravitational lens effect as a “natural telescope”.

In the 1960s, a few partly independent theoretical studies showed the usefulness of lensing for astronomy [95111112123146147Jump To The Next Citation Point]. In particular, Sjur Refsdal derived the basic equations of gravitational lens theory and subsequently showed how the gravitational lens effect can be used to determine Hubble’s constant by measuring the time delay between two lensed images. He followed up this work with interesting applications of lensing [149148150]. The mathematical foundation of how a light bundle is distorted on its passage through the universe had been derived in the context of gravitational radiation even before [157].

Originally, gravitational lensing was discussed for stars or for galaxies. When quasars were discovered in the 1960s, Barnothy [14] was the first to connect them with the gravitational lens effect. In the late 60s/early 70s, a few groups and individuals explored various aspects of lensing further, for example, statistical effects of local inhomogeneities on the propagation of light [71Jump To The Next Citation Point72Jump To The Next Citation Point143]; lensing applied to quasars and clusters of galaxies [42130158]; development of a formalism for transparent lenses [3040]; and the effect of an inhomogeneous universe on the distance-redshift relations [46].

But only in 1979 did the whole field receive a real boost when the first double quasar was discovered and confirmed to be a real gravitational lens by Walsh, Carswell & Weymann [193Jump To The Next Citation Point]. This discovery, and the development of lensing since then, will be described in Section 4.

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