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While gravitational lensing preserves surface brightness, as dictated by Liouville's theorem, lensing does change the apparent solid angle of a source. The amount of magnification is given by the ratio of the image area to the source area. For a circularly symmetric lens, the magnification factor μ is given by
For a source right behind the lens, θ S = 0, the lens equation for a point mass gives a characteristic value for θ 1 that is called the Einstein angle, denoted θ E. When θ E is expressed in radians, and the lensing source is sufficiently far away, the Einstein Radius, denoted R E, is given by =. [2]
The amount of gravitational lensing is described by Albert Einstein's general theory of relativity. [ 1 ] [ 2 ] If light is treated as corpuscles travelling at the speed of light , Newtonian physics also predicts the bending of light, but only half of that predicted by general relativity.
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
In the context of general relativity, it means the problem of finding solutions to Einstein's field equations — a system of hyperbolic partial differential equations — given some initial data on a hypersurface. Studying the Cauchy problem allows one to formulate the concept of causality in general relativity, as well as 'parametrising ...
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.
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.
Since giving the Einstein tensor does not fully determine the Riemann tensor, but leaves the Weyl tensor unspecified (see the Ricci decomposition), the Einstein equation may be considered a kind of compatibility condition: the spacetime geometry must be consistent with the amount and motion of any matter or non-gravitational fields, in the ...