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BTZ Black Hole
The BTZ black hole, named after Máximo Bañados, Claudio Teitelboim, and Jorge Zanelli, is a black hole solution for (2+1)-dimensional topological gravity with a negative cosmological constant. History In 1992, Bañados, Teitelboim, and Zanelli discovered the BTZ black hole solution . This came as a surprise, because when the cosmological constant is zero, a vacuum solution of (2+1)-dimensional gravity is necessarily flat (the Weyl tensor vanishes in three dimensions, while the Ricci tensor vanishes due to the Einstein field equations, so the full Riemann tensor vanishes), and it can be shown that no black hole solutions with event horizons exist. But thanks to the negative cosmological constant in the BTZ black hole, it is able to have remarkably similar properties to the 3+1 dimensional Schwarzschild and Kerr black hole solutions, which model real-world black holes. Properties The similarities to the ordinary black holes in 3+1 dimensions: * It admits a no hair theorem, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Máximo Bañados
Maximo or Máximo may refer to: Arts * Capcom video game series ** '' Maximo: Ghosts to Glory'' (also known as just ''Maximo'') ** '' Maximo vs. Army of Zin'', the sequel to ''Ghosts to Glory'' * Maxïmo Park, a British indie rock band * Maximu or Maximo, a legendary female warrior descended from the Amazons who is killed by Basil Digenes Akritas People * Joel and Jose Maximo, a wrestling tag team known as The S.A.T. * Máximo (wrestler) (born 1980), ring name of Mexican wrestler José Christian Nieves Ruiz * Maximo Blanco (born 1983), Venezuelan professional Mixed Martial Artist * Máximo Gómez (1836–1905), military commander of the Cuba independence campaign * Máximo Macapobre, Filipino activist and the founder of Toledo City, Philippines * Máximo Rigondeaux (born 1976), Cuban javelin thrower * Máximo Santos (1847–1889), Uruguay president * Máximo Tajes (1852–1912), Uruguay president * Maximo V. Lorenzo (born 1982), comic artist. * Maximo V. Soliven, Filipino ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newtonian Limit
In physics, the Newtonian limit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly compared to the speed of light, and (3) slowly changing (or completely static) gravitational fields. Under these conditions, Newton's law of universal gravitation may be used to obtain values that are accurate. In general, and in the presence of significant gravitation, the general theory of relativity must be used. In the Newtonian limit, spacetime is approximately flat and the Minkowski metric may be used over finite distances. In this case 'approximately flat' is defined as space in which gravitational effect approaches 0, mathematically actual spacetime and Minkowski space are not identical, Minkowski space is an idealized model. Special relativity In special relativity, Newtonian behaviour can in most cases be obtained by performing the limit v\to 0 . In this limit, the often appearing gamma factor becomes 1 \begin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Holes
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. A black hole has a great effect on the fate and circumstances of an object crossing it, but has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AdS Black Hole
In theoretical physics, an anti-de Sitter (AdS) black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a negative cosmological constant. Such a solution asymptotically approaches anti-de Sitter space at spatial infinity, and is a generalization of the Kerr vacuum solution, which asymptotically approaches Minkowski spacetime at spatial infinity. In 3+1 dimensions, the metric is given by ds^2 = - \left( k^2r^2 + 1 - \frac \right)dt^2 + \fracdr^2 + r^2 d\Omega^2 where is the time coordinate, is the radial coordinate, are the polar coordinates, is a constant and is the AdS curvature. In general, in dimensions, the metric is given by ds^2 = - \left( k^2r^2 + 1 - \frac \right)dt^2 + \fracdr^2 + r^2 d\Omega^2 According to the AdS/CFT correspondence, if gravity were quantized, an AdS black hole would be dual to a thermal state on the conformal boundary. In the context of say, AdS/QCD, this would correspon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MTZ Black Hole
The MTZ black hole, named after Cristian Martinez, Ricardo Troncoso and Jorge Zanelli, is a black hole solution for (3+1)-dimensional gravity with a minimally coupled self-interacting scalar field In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical .... The event horizon is a surface of constant negative curvature, and the spacetime is asymptotically locally anti-de Sitter. See also * BTZ black hole References * The original MTZ-paper Quantum gravity Mathematical methods in general relativity Black holes {{black-hole-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosmic String
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected. In less formal terms, they are hypothetical long, thin defects in the fabric of space that might have formed according to string theory. They might have formed in the early universe during a process where certain symmetries were broken. Their existence was first contemplated by the theoretical physicist Tom Kibble in the 1970s. The formation of cosmic strings is somewhat analogous to the imperfections that form between crystal grains in solidifying liquids, or the cracks that form when water freezes into ice. The phase transitions leading to the production of cosmic strings are likely to have occurred during the earliest moments of the universe's evolution, just after cosmological inflation, and are a fairly generic predic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Timelike Curve
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949,Stephen Hawking, '' My Brief History'', chapter 11 who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Covering Space
In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto itself. In particular, coverings are special types of local homeomorphisms. If p : \tilde X \to X is a covering, (\tilde X, p) is said to be a covering space or cover of X, and X is said to be the base of the covering, or simply the base. By abuse of terminology, \tilde X and p may sometimes be called covering spaces as well. Since coverings are local homeomorphisms, a covering space is a special kind of étalé space. Covering spaces first arose in the context of complex analysis (specifically, the technique of analytic continuation), where they were introduced by Riemann as domains on which naturally multivalued complex functions become single-valued. These spaces are now called Riemann surfaces. Covering spaces are an important tool in several areas of mathematics. In modern geometry, covering spaces (or b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbifold
In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space. Definitions of orbifold have been given several times: by Ichirō Satake in the context of automorphic forms in the 1950s under the name ''V-manifold''; by William Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name ''orbifold'', after a vote by his students; and by André Haefliger in the 1980s in the context of Mikhail Gromov's programme on CAT(k) spaces under the name ''orbihedron''. Historically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms with the action of the modular group \mathrm(2,\Z) on the upper half-plane: a version of the Riemann–Roch theorem holds after the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anti-de Sitter Space
In mathematics and physics, ''n''-dimensional anti-de Sitter space (AdS''n'') is a symmetric_space, maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (6 May 1872 – 20 November 1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe. Paul Dirac was the first person to rigorously explore anti-de Sitter space, doing so in 1963. Manifolds of constant curvature are most familiar in the case of two dimensions, where the elliptic plane or surface of a sphere is a surface of constant positive curvature, a flat (i.e., Euclidean space, Euclidean) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature. Einstein's general theory of relat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang. Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the Electromagnetism, electromagnetic interaction, the Strong interaction, strong force, and the Weak interaction, weak force; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Collapse
Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formation in the universe. Over time an initial, relatively smooth distribution of matter, after sufficient accretion, may collapse to form pockets of higher density, such as stars or black holes. Star formation involves a gradual gravitational collapse of interstellar medium into clumps of molecular clouds and potential protostars. The compression caused by the collapse raises the temperature until thermonuclear fusion occurs at the center of the star, at which point the collapse gradually comes to a halt as the outward thermal pressure balances the gravitational forces. The star then exists in a state of dynamic equilibrium. During the star's evolution a star might collapse again and reach several new states of equilibrium. Star formation A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
