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Einstein–Rosen Metric
The Einstein–Rosen metric is an exact solution of Einstein's field equation. It was derived by Albert Einstein and Nathan Rosen in 1937. It is the first exact solution of Einstein's equation that described the propagation of a gravitational wave. This metric can be written in a form such that the Belinski–Zakharov transform applies, and thus has the form of a gravitational soliton A gravitational soliton is a soliton solution of the Einstein field equation. It can be separated into two kinds, a soliton of the vacuum Einstein field equation generated by the Belinski–Zakharov transform, and a soliton of the Einstein–Maxwe .... In 1972 and 1973, J. R. Rao, A. R. Roy, and R. N. Tiwari published a class of exact solutions involving the Einstein-Rosen metric.\ In 2021 Robert F. Penna found an algebraic derivation of the Einstein-Rosen metric. In the history of science, one might consider as a footnote to the Einstein-Rosen metric that Einstein, for some time, believed that he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein's Field Equation
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form of a tensor equation which related the local ' (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor). Analogously to the way that electromagnetic fields are related to the distribution of charges and currents via Maxwell's equations, the EFE relate the spacetime geometry to the distribution of mass–energy, momentum and stress, that is, they determine the metric tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of nonlinear partial differential equations when used in this way. The solutions of the EFE ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory of relativity, but he also made important contributions to the development of the theory of quantum mechanics. Relativity and quantum mechanics are the two pillars of modern physics. His mass–energy equivalence formula , which arises from relativity theory, has been dubbed "the world's most famous equation". His work is also known for its influence on the philosophy of science. He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory. His intellectual achievements and originality resulted in "Einstein" becoming synonymous with "genius". In 1905, a year sometimes described as his ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nathan Rosen
Nathan Rosen (Hebrew: נתן רוזן; March 22, 1909 – December 18, 1995) was an American-Israeli physicist noted for his study on the structure of the hydrogen atom and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox. The Einstein–Rosen bridge, later named the wormhole, was a theory of Nathan Rosen. Background Nathan Rosen was born into a Jewish family in Brooklyn, New York. He attended MIT during the Great Depression, where he received a bachelor's degree in electromechanical engineering and later a master's and a doctorate in physics. As a student he published several papers of note, one being "The Neutron," which attempted to explain the structure of the atomic nucleus a year before their discovery by James Chadwick. He also developed an interest in wave functions, and later, gravitation, when he worked as a fellow at the University of Michigan and Princeton University. State of science At the beginning of the 20th century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Wave
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as waves similar to electromagnetic waves but the gravitational equivalent. Gravitational waves were later predicted in 1916 by Albert Einstein on the basis of his general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed)showing one of the ways the methods of Newtonian physics are unable to explain ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belinski–Zakharov Transform
The Belinski–Zakharov (inverse) transform is a nonlinear transformation that generates new exact solutions of the vacuum Einstein's field equation. It was developed by Vladimir Belinski and Vladimir Zakharov in 1978. The Belinski–Zakharov transform is a generalization of the inverse scattering transform. The solutions produced by this transform are called gravitational solitons (gravisolitons). Despite the term 'soliton' being used to describe gravitational solitons, their behavior is very different from other (classical) solitons. In particular, gravitational solitons do not preserve their amplitude and shape in time, and up to June 2012 their general interpretation remains unknown. What is known however, is that most black holes (and particularly the Schwarzschild metric and the Kerr metric) are special cases of gravitational solitons. Introduction The Belinski–Zakharov transform works for spacetime intervals of the form :: ds^2 = f (-d(x^0)^2 + d(x^1)^2) + g_ \, dx^a \, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Soliton
A gravitational soliton is a soliton solution of the Einstein field equation. It can be separated into two kinds, a soliton of the vacuum Einstein field equation generated by the Belinski–Zakharov transform, and a soliton of the Einstein–Maxwell equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ... generated by the Belinski-Zakharov-Alekseev transform. References General relativity {{relativity-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Physics
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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