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Eddington–Finkelstein Coordinates
In general relativity, Eddington–Finkelstein coordinates are a pair of coordinate systems for a Schwarzschild geometry (e.g. a spherically symmetric black hole) which are adapted to radial null geodesics. Null geodesics are the worldlines of photons; radial ones are those that are moving directly towards or away from the central mass. They are named for Arthur Stanley Eddington and David Finkelstein. Although they appear to have inspired the idea, neither ever wrote down these coordinates or the metric in these coordinates. Roger Penrose seems to have been the first to write down the null form but credits it to the above paper by Finkelstein, and, in his Adams Prize essay later that year, to Eddington and Finkelstein. Most influentially, Misner, Thorne and Wheeler, in their book '' Gravitation'', refer to the null coordinates by that name. In these coordinate systems, outward (inward) traveling radial light rays (which each follow a null geodesic) define the surfaces of consta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lemaître Coordinates
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. English translation: See also: … Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius. Equations The original Schwarzschild coordinate expression of the Schwarzschild metric, in natural units (), is given as :ds^2=\left(1-\right)dt^2- - r^2\left(d\theta^2+\sin^2\theta d\phi^2\right) \;, where :ds^2 is the invariant interval; :r_s=\frac is the Schwarzschild radius; :M is the mass of the central body; :t, r, \theta, \phi are the Schwarzschild coordinates (which asymptotically turn into the flat spherical coordinates); :c is the speed of light; :and G is the gravitational constant. This metric has a coordinate singularity at the Schwarzschild radius r=r_s. Georges Lemaître was the first to show t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
