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An Einstein Ring is a special case of gravitational lensing, caused by the exact alignment of the source, lens, and observer. This results in symmetry around the lens, causing a ring-like structure. [2] The geometry of a complete Einstein ring, as caused by a gravitational lens. The size of an Einstein ring is given by the Einstein radius.
Albert Einstein. Relativity: the Special and the General Theory, 10th edition (there are a total of 17 editions). ISBN 0-517-029618 at Project Gutenberg; Relativity: The Special and General Theory public domain audiobook at LibriVox; Albert Einstein, Relativity: The Special and General Theory (1920/2000) ISBN 1-58734-092-5 at Bartleby.com
The same value as Soldner's was calculated by Einstein in 1911 based on the equivalence principle alone. [13]: 3 However, Einstein noted in 1915, in the process of completing general relativity, that his (and thus Soldner's) 1911-result is only half of the correct value. Einstein became the first to calculate the correct value for light bending.
A(u) always decreases as u increases, so the closer the alignment, the brighter the source becomes. As u approaches infinity, A(u) approaches 1, so that at wide separations, microlensing has no effect. Finally, as u approaches 0, for a point source A(u) approaches infinity as the images approach an Einstein ring.
A new photograph from the Hubble Space Telescope shows a stunning “Einstein Ring” billions of light-years from Earth — a phenomenon named after Albert Einstein.
For a dense cluster with mass M c ≈ 10 × 10 15 M ☉ at a distance of 1 Gigaparsec (1 Gpc) this radius could be as large as 100 arcsec (called macrolensing). For a Gravitational microlensing event (with masses of order 1 M ☉) search for at galactic distances (say D ~ 3 kpc), the typical Einstein radius would be of order milli-arcseconds ...
Einstein explained his goal in the preface of the book's German edition by stating he "wanted to summarize the principal thoughts and mathematical methods of relativity theory" and that his "principal aim was to let the fundamentals in the entire train of thought of the theory emerge clearly". [1]
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