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Aichelburg–Sexl Ultraboost
In general relativity, the Aichelburg–Sexl ultraboost is an exact solution which models the spacetime of an observer moving towards or away from a spherically symmetric gravitating object at nearly the speed of light. It was introduced by Peter C. Aichelburg and Roman U. Sexl in 1971. The original motivation behind the ultraboost was to consider the gravitational field of massless point particles within general relativity. It can be considered an approximation to the gravity well of a photon or other lightspeed particle, although it does not take into account quantum uncertainty in particle position or momentum. The metric tensor can be written, in terms of Brinkmann coordinates, as : ds^2 = -8m \, \delta(u) \, \log r \, du^2 + 2 \, du \, dv + dr^2 + r^2 \, d\theta^2, : -\infty < u,v < \infty, \, 0 < r < \infty, \, -\pi < \theta < \pi The ultraboost can be obtained as the limit of a metric, which is also an exact solution, at least if one admits impulsive curvature ... [...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] |
Exact Solutions In General Relativity
In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field. Background and definition These tensor fields should obey any relevant physical laws (for example, any electromagnetic field must satisfy Maxwell's equations). Following a standard recipe which is widely used in mathematical physics, these tensor fields should also give rise to specific contributions to the stress–energy tensor T^. (A field is described by a Lagrangian, varying with respect to the field should give the field equations and varying with respect to the metric should give the stre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwarzschild Metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916, and around the same time independently by Johannes Droste, who published his more complete and modern-looking discussion four months after Schwarzschild. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum. A Schwar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter C
Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a surname (including a list of people with the name) Culture * Peter (actor) (born 1952), stage name Shinnosuke Ikehata, Japanese dancer and actor * ''Peter'' (album), a 1993 EP by Canadian band Eric's Trip * ''Peter'' (1934 film), a 1934 film directed by Henry Koster * ''Peter'' (2021 film), Marathi language film * "Peter" (''Fringe'' episode), an episode of the television series ''Fringe'' * ''Peter'' (novel), a 1908 book by Francis Hopkinson Smith * "Peter" (short story), an 1892 short story by Willa Cather Animals * Peter, the Lord's cat, cat at Lord's Cricket Ground in London * Peter (chief mouser), Chief Mouser between 1929 and 1946 * Peter II (cat), Chief Mouser between 1946 and 1947 * Peter III (cat), Chief Mouser between 1947 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman U
Roman or Romans most often refers to: * Rome, the capital city of Italy * Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *''Epistle to the Romans'', shortened to ''Romans'', a letter in the New Testament of the Christian Bible Roman or Romans may also refer to: Arts and entertainment Music *Romans (band), a Japanese pop group * ''Roman'' (album), by Sound Horizon, 2006 * ''Roman'' (EP), by Teen Top, 2011 *"Roman (My Dear Boy)", a 2004 single by Morning Musume Film and television *Film Roman, an American animation studio * ''Roman'' (film), a 2006 American suspense-horror film * ''Romans'' (2013 film), an Indian Malayalam comedy film * ''Romans'' (2017 film), a British drama film * ''The Romans'' (''Doctor Who''), a serial in British TV series People * Roman (given name), a given name, including a list of people and fictional characters * Roman (surname), including a list of people named Roman or Romans *ῬωμΠ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Tensor
In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a point of is a bilinear form defined on the tangent space at (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric tensor on consists of a metric tensor at each point of that varies smoothly with . A metric tensor is ''positive-definite'' if for every nonzero vector . A manifold equipped with a positive-definite metric tensor is known as a Riemannian manifold. Such a metric tensor can be thought of as specifying ''infinitesimal'' distance on the manifold. On a Riemannian manifold , the length of a smooth curve between two points and can be defined by integration, and the distance between and can be defined as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brinkmann Coordinates
Brinkmann coordinates are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. They are named for Hans Brinkmann. In terms of these coordinates, the metric tensor can be written as :ds^2 = H(u,x,y) du^2 + 2 du dv + dx^2 + dy^2 where \partial_, the coordinate vector field dual to the covector field dv, is a null vector field. Indeed, geometrically speaking, it is a null geodesic congruence with vanishing optical scalars. Physically speaking, it serves as the wave vector defining the direction of propagation for the pp-wave. The coordinate vector field \partial_ can be spacelike, null, or timelike at a given event in the spacetime, depending upon the sign of H(u,x,y) at that event. The coordinate vector fields \partial_, \partial_ are both spacelike vector fields. Each surface u=u_, v=v_ can be thought of as a wavefront. In discussions of exact solutions to the Einstein field equation, many authors fail to specify the intended ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., f(x)) to its value at zero of its domain (f(0)), or as the weak limit of a sequence of bump functions (e.g., \delta(x) = \lim_ \frace^), which are zero over most of the real line, with a tall spike at the origin. Bump functions are thus sometimes called "approximate" or "nascent" delta distributions. The delta function was introduced by physicist Paul Dirac as a tool for the normalization of state vectors. It also has uses in probability theory and signal processing. Its validity was disputed until Laurent Schwartz developed the theory of distributions where it is defined as a linear form acting on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
