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Kantowski–Sachs Metric
In general relativity the Kantowski-Sachs metric (named after Ronald Kantowski and Rainer K. Sachs) describes a homogeneous but anisotropic universe whose spatial section has the topology of \mathbb \times S^. The metric is: : ds^ = -dt^ + e^ dz^ + \frac(d\theta^ + \sin^\theta d\phi^) The isometry group of this spacetime is \mathbb \times SO(3). Remarkably, the isometry group does not act simply transitively on spacetime, nor does it possess a subgroup with simple transitive action. See also * Bianchi classification *Dust solution In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has ' ... Notes General relativity Physical cosmology {{relativity-stub ... [...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] |
Ronald Kantowski
Ronald Kantowski (18 December 1939) is a theoretical cosmologist, well known in the field of general relativity as the author, together with Rainer K. Sachs, of the Kantowski–Sachs dust solutions to the Einstein field equation. These are a widely used family of inhomogeneous cosmological models. Life and career Kantowski received his Ph.D. in 1966 from the University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ..., where he wrote a dissertation on cosmological models. He was a research scientist at the South West Center for Advanced Studies during 1967–1968. He was hired by the Physics & Astronomy department of the University of Oklahoma in 1968, where he became a full professor in 1981. Besides the Kantowski–Sachs solutions to the Einstein's field e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rainer K
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Rainer may refer to: People * Rainer (surname) * Rainer (given name) Other * Rainer Island, an island in Franz Josef Land, Russia * 16802 Rainer, an asteroid * Rainer Foundation, British charitable organisation See also * Rainier (other) * Rayner (other) * Raynor * Reiner (other) * Reyner Reyner is a surname, and has also been used as a given name. Notable people with the name include: * Reyner Banham (1922–1988), English architectural critic * Clement Reyner (1589–1651), English Benedictine monk * Edward Reyner (1600–c.16 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous
Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous is distinctly nonuniform in at least one of these qualities. Etymology and spelling The words ''homogeneous'' and ''heterogeneous'' come from Medieval Latin ''homogeneus'' and ''heterogeneus'', from Ancient Greek ὁμογενής (''homogenēs'') and ἑτερογενής (''heterogenēs''), from ὁμός (''homos'', "same") and ἕτερος (''heteros'', "other, another, different") respectively, followed by γένος (''genos'', "kind"); -ous is an adjectival suffix. Alternate spellings omitting the last ''-e-'' (and the associated pronunciations) are common, but mistaken: ''homogenous'' is strictly a biological/pathological term whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anisotropic
Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical property, physical or list of materials properties#Mechanical properties, mechanical properties when measured along different axes, e.g. absorbance, refractive index, electrical resistivity and conductivity, conductivity, and tensile strength. An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its wood grain, grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions). Fields of interest Computer graphics In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its normal (geometry), geometric normal, as is the case with velvet. Anisotropic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' meaning "equal", and μέτρον ''metron'' meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion. Introduction Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional Euclidean space, two geometric figures are congruent if they are related by an isometry; the isometry that relates them is either a rigid motion (translation or rotati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bianchi Classification
In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras (up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized family of Lie algebras. (Sometimes two of the groups are included in the infinite families, giving 9 instead of 11 classes.) The classification is important in geometry and physics, because the associated Lie groups serve as symmetry groups of 3-dimensional Riemannian manifolds. It is named for Luigi Bianchi, who worked it out in 1898. The term "Bianchi classification" is also used for similar classifications in other dimensions and for classifications of complex Lie algebras. Classification in dimension less than 3 * Dimension 0: The only Lie algebra is the abelian Lie algebra R0. * Dimension 1: The only Lie algebra is the abelian Lie algebra R1, with outer automorphism group the multiplicative group of non-zero real numbers. * Dimensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dust Solution
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has ''positive mass density'' but ''vanishing pressure''. Dust solutions are an important special case of fluid solutions in general relativity. Dust model A perfect and pressureless fluid can be interpreted as a model of a configuration of ''dust particles'' that locally move in concert and interact with each other only gravitationally, from which the name is derived. For this reason, dust models are often employed in cosmology as models of a toy universe, in which the dust particles are considered as highly idealized models of galaxies, clusters, or superclusters. In astrophysics, dust models have been employed as models of gravitational collapse. Dust solutions can also be used to model finite rotating disks of dust grains; some examples ... [...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] |
