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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 general relativity, the Einstein–Rosen metric is an exact solution to the Einstein field equations derived in 1937 by Albert Einstein and Nathan Rosen. [1] It is the first exact solution to describe the propagation of a gravitational wave .
The odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. The theorem states that the number of multiple images produced by a bounded transparent lens must be odd .
Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise. Novel techniques developed by numerical relativity ...
Some teams argued to further reduce the budget cap to $100 million, citing concerns that the long-term financial impact of the COVID-19 pandemic threatens the future of as many as four teams. [114] [115] Formula One managing director Ross Brawn stated that the sport's intention is to reduce the budget cap further in the coming years. [112]