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Weyl–Lewis–Papapetrou Coordinates
In general relativity, the Weyl–Lewis–Papapetrou coordinates are used in solutions to the vacuum region surrounding an axisymmetric distribution of mass–energy. They are named for Hermann Weyl, Thomas Lewis, and Achilles Papapetrou. Details The square of the line element is of the form: :ds^2 = -e^dt^2 + \rho^2 B^2 e^(d\phi - \omega dt)^2 + e^(d\rho^2 + dz^2) where (t, \rho, \phi, z) are the cylindrical Weyl–Lewis–Papapetrou coordinates in 3+1 -dimensional spacetime, and \lambda , \nu , \omega , and B , are unknown functions of the spatial non-angular coordinates \rho and z only. Different authors define the functions of the coordinates differently. See also *Introduction to the mathematics of general relativity *Stress–energy tensor *Metric tensor (general relativity) *Relativistic angular momentum *Weyl metrics In general relativity, the Weyl metrics (named after the German-American mathematician Hermann Weyl) are a class of ''static'' and ''axisymmetric'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General theory of relativity, 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 in physics, time, or four-dimensional spacetime. In particular, the ''curvature of spacetime'' is directly related to the energy and momentum of whatever is present, including matter and radiation. 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 gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weyl Metrics
In general relativity, the Weyl metrics (named after the German-American mathematician Hermann Weyl) are a class of ''static'' and ''axisymmetric'' solutions to Einstein's field equation. Three members in the renowned Kerr–Newman family solutions, namely the Schwarzschild, nonextremal Reissner–Nordström and extremal Reissner–Nordström metrics, can be identified as Weyl-type metrics. Standard Weyl metrics The Weyl class of solutions has the generic formJeremy Bransom Griffiths, Jiri Podolsky. ''Exact Space-Times in Einstein's General Relativity''. Cambridge: Cambridge University Press, 2009. Chapter 10.Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers, Eduard Herlt. ''Exact Solutions of Einstein's Field Equations''. Cambridge: Cambridge University Press, 2003. Chapter 20. where \psi(\rho,z) and \gamma(\rho,z) are two metric potentials dependent on ''Weyl's canonical coordinates'' \. The coordinate system \ serves best for symmetries of Weyl's space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Charts In General Relativity
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the Position (geometry), position of the Point (geometry), points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line (geometry), line with real numbers using the ''number line''. In this system, an arbitrary point ''O'' (the ''ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
