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Horndeski's Theory
Horndeski's theory is the most general theory of gravity in four dimensions whose Lagrangian is constructed out of the metric tensor and a scalar field and leads to second order equations of motion. The theory was first proposed by Gregory Horndeski in 1974 and has found numerous applications, particularly in the construction of cosmological models of Inflation and dark energy. Horndeski's theory contains many theories of gravity, including general relativity, Brans–Dicke theory, quintessence, dilaton, chameleon particle and covariant Galileon as special cases. Action Horndeski's theory can be written in terms of an action as S _,\phi= \int\mathrm^x\,\sqrt\left _,\phi.html" ;"title="sum_^\frac\mathcal_[g_,\phi">sum_^\frac\mathcal_[g_,\phi,+\mathcal_[g_,\psi_right] with the Lagrangian (field theory), Lagrangian densities \mathcal_ = G_(\phi,\, X) \mathcal_ = G_(\phi,\,X)\Box\phi \mathcal_ = G_(\phi,\,X)R+G_(\phi,\,X)\left left(\Box\phi\right)^-\phi_\phi^\right/math> \ ... [...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 field 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] |
Scalar Curvature
In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls. In the context of the differential geometry of surfaces, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface. In higher dimensions, however, the scalar curvature only represents one particular part of the Riemann curvature tensor. The definition of scalar curvature via partial derivatives is also valid in the more general setting of pseudo-Riemannian manifolds. This is significant in general relativity, where scalar curvature of a Lorentzian metric is one of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lovelock Theory Of Gravity
In theoretical physics, Lovelock's theory of gravity (often referred to as Lovelock gravity) is a generalization of Einstein's theory of general relativity introduced by David Lovelock in 1971. It is the most general metric theory of gravity yielding conserved second order equations of motion in an arbitrary number of spacetime dimensions ''D''. In this sense, Lovelock's theory is the natural generalization of Einstein's general relativity to higher dimensions. In three and four dimensions (''D'' = 3, 4), Lovelock's theory coincides with Einstein's theory, but in higher dimensions the theories are different. In fact, for ''D'' > 4 Einstein gravity can be thought of as a particular case of Lovelock gravity since the Einstein–Hilbert action is one of several terms that constitute the Lovelock action. Lagrangian density The Lagrangian of the theory is given by a sum of dimensionally extended Euler densities, and it can be written as follows : \mathcal=\sqrt\ \sum\limits_^\alph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massive Gravity
Massive is an adjective related to mass. Massive may refer to: Arts, entertainment, and media * Massive (band), an Australian Hard Rock band * ''Massive'', an album by The Supervillains released in 2008 * Massive Attack, a British musical group, who were temporarily known as Massive in 1991 * Massive (song), "Massive" (song), a song by Drake from the 2022 album ''Honestly, Nevermind'' * Massive (TV series), ''Massive'' (TV series), a situation comedy first aired on BBC3 in September 2008 * Massive! (TV programme), ''Massive!'' (TV programme), a short-lived Saturday morning British television programme (1995–1996) * ''MMO Games Magazine'', formerly ''MASSIVE Magazine'', a short-lived computer magazine * ''Massive: Gay Erotic Manga and the Men Who Make It'', a 2014 manga anthology * The Massive (comics), ''The Massive'' (comics), an ongoing comic series * The Massive, a starship in the U.S. animated television series ''Invader Zim'' * Massive, the villain in ''Loonatics Unleashe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Graviton
In theoretical physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric–magnetic duality, as an S-duality, predicted by some formulations of eleven-dimensional supergravity. The dual graviton was first hypothesized in 1980. It was theoretically modeled in 2000s, which was then predicted in eleven-dimensional mathematics of SO(8) supergravity in the framework of electric–magnetic duality. It again emerged in the ''E''11 generalized geometry in eleven dimensions, and the ''E''7 generalized vielbein-geometry in eleven dimensions. While there is no local coupling between graviton and dual graviton, the field introduced by dual graviton may be coupled to a BF model as non-local gravitational fields in extra dimensions. A ''massive'' dual gravity of Ogievetsky–Polubarinov model can be obtained by coupling the dual graviton field to the curl of its own energy-momentum tensor. The previously mentioned theories of dual ... [...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] |
Classical Theories Of Gravitation
Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory of general relativity. There have been many different attempts at constructing an ideal theory of gravity. These attempts can be split into four broad categories based on their scope: # Classical theories of gravity, which do not involve quantum mechanics or force unification. # Theories using the principles of quantum mechanics resulting in quantized gravity. # Theories which attempt to explain gravity and other forces at the same time; these are known as classical unified field theories. # Theories which attempt to both put gravity in quantum mechanical terms and unify forces; these are called theories of everything. None of these alternatives to general relativity have gained wide acceptance. General relativity has withstood many tests over a large range of mass and size scales. When applied to interpret astronomical observati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GW170817
GW170817 was a gravitational wave (GW) observed by the LIGO and Virgo detectors on 17 August 2017, originating within the shell elliptical galaxy NGC 4993, about 144 million light years away. The wave was produced by the last moments of the inspiral of a binary pair of neutron stars, ending with their merger. , it is the only GW detection to be definitively correlated with any electromagnetic observation. Unlike the five prior GW detections—which were of merging black holes and thus not expected to have detectable electromagnetic signals—the aftermath of this merger was seen across the electromagnetic spectrum by 70 observatories on 7 continents and in space, marking a significant breakthrough for multi-messenger astronomy. The discovery and subsequent observations of GW170817 were given the Breakthrough of the Year award for 2017 by the journal ''Science''. GW170817 had an audible duration of approximately 100 seconds and exhibited the characteristic intensity an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ATLAS Experiment
ATLAS is the largest general-purpose particle detector experiment at the Large Hadron Collider (LHC), a particle accelerator at CERN (the European Organization for Nuclear Research) in Switzerland. The experiment is designed to take advantage of the unprecedented energy available at the LHC and observe phenomena that involve highly massive particles which were not observable using earlier lower-energy accelerators. ATLAS was one of the two LHC experiments involved in the discovery of the Higgs boson in July 2012. It was also designed to search for evidence of theories of particle physics beyond the Standard Model. The experiment is a collaboration involving 6,003 members, out of which 3,822 are physicists (last update: June 26, 2022) from 243 institutions in 40 countries. History Particle accelerator growth The first cyclotron, an early type of particle accelerator, was built by Ernest O. Lawrence in 1931, with a radius of just a few centimetres and a particle energy of 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Notation
In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity. As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in physics applications that do not distinguish between tangent and cotangent spaces. It was introduced to physics by Albert Einstein in 1916. Introduction Statement of convention According to this convention, when an index variable appears twice in a single term and is not otherwise defined (see Free and bound variables), it implies summation of that term over all the values of the index. So where the indices can range over the set , y = \sum_^3 x^i e_i = x^1 e_1 + x^2 e_2 + x^3 e_3 is simplified by the convention to: y = x^i e_i The upper indices are not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariant Derivative
In mathematics and physics, covariance is a measure of how much two variables change together, and may refer to: Statistics * Covariance matrix, a matrix of covariances between a number of variables * Covariance or cross-covariance between two random variables or data sets * Autocovariance, the covariance of a signal with a time-shifted version of itself * Covariance function, a function giving the covariance of a random field with itself at two locations Algebra and geometry * A covariant (invariant theory) is a bihomogeneous polynomial in and the coefficients of some homogeneous form in that is invariant under some group of linear transformations. * Covariance and contravariance of vectors, properties of how vector coordinates change under a change of basis ** Covariant transformation, a rule that describes how certain physical entities change under a change of coordinate system * Covariance and contravariance of functors, properties of functors * General covariance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
