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Post-Minkowskian Expansion
In physics, precisely in the general theory of relativity, post-Minkowskian expansions (PM) or post-Minkowskian approximations are mathematical methods used to find approximate solutions of Einstein's equations by means of a power series development of the metric tensor. Unlike post-Newtonian expansions (PN), in which the series development is based on a combination of powers of the velocity (which must be negligible compared to that of light) and the gravitational constant, in the post-Minkowskian case the developments are based only on the gravitational constant, allowing analysis even at velocities close to that of light (relativistic). One of the earliest works on this method of resolution is that of Bruno Bertotti Bruno Bertotti (24 December 1930 – 20 October 2018) was an Italian physicist, emeritus professor at the University of Pavia. He was one of the last students of physicist Erwin Schrödinger. Bertotti was well known for his contributions to gener ..., publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PM Vs PN Expansion EN
PM or pm (also written P.M. or p.m.) is an abbreviation for Latin ''post meridiem'', meaning "after midday" in the 12-hour clock. PM or Pm or pm may also refer to: Arts and entertainment *Palm mute, a guitar playing technique * ''PM'' (Australian radio program) * ''PM'' (BBC Radio 4), UK *''PM Magazine'', an American TV news program (1976–1991). * ''PM'' (newspaper), US (1940–1948) *PM Press, an American publishing company *Project Mayhem, a “fictional conspiracy” created in the Chuck Palahniuk 1996 novel Fight Club and 1999 movie of the same name * PM a rock band featuring british drummer Carl Palmer. Business and economics Businesses *P.M. Place Stores, a former US chain of discount stores *Pere Marquette Railway, North America 1900–1947, reporting mark *Philip Morris International, a tobacco company Terminology *Performance management of an organisation *Portfolio manager *Preventive maintenance *Project manager *Product manager Government *Prime minister *Políci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Theory Of Relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, 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 space, 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 distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein's 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 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] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...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] |
Post-Newtonian Expansion
In general relativity, the post-Newtonian expansions (PN expansions) are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of deviations from Newton's law of universal gravitation. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher order terms can be added to increase accuracy, but for strong fields sometimes it is preferable to solve the complete equations numerically. This method is a common mark of effective field theories. In the limit, when the small parameters are equal to 0, the post-Newtonian expansion reduces to Newton's law of gravity. Expansion in 1/''c''2 The post-Newtonian approximations are expansions in a small parameter, which is the ratio of the velocity of the matter that creates the gravitational field, to the speed of light, which in this case is more precisely called the ''speed of gravity''. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Starlight viewed on Earth left the stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for signals to travel from Earth to the spacecraft and vice versa. In computing, the speed of light fixes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately The modern notation of Newton's law involving was introduced in the 1890s by C. V. Boys. The first impl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Space
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be implied by the postulates of special relativity. Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events.This makes spacetime distance an invariant. Becaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruno Bertotti
Bruno Bertotti (24 December 1930 – 20 October 2018) was an Italian physicist, emeritus professor at the University of Pavia. He was one of the last students of physicist Erwin Schrödinger. Bertotti was well known for his contributions to general relativity – particularly the Bertotti-Robinson electrovacuum, an exact solution of the Einstein field equation. He has also obtained a more accurate measurement of the parameter gamma of the parameterized post-Newtonian formalism, with the Cassini radioscience experiment. The PPN gamma parameter measures the curvature of space in the metric theory of gravitation and it is equal to one in general relativity. More recent studies revealed that the measured value of the PPN parameter gamma is affected by gravitomagnetic effect caused by the orbital motion of Sun around the barycenter of the solar system. The gravitomagnetic effect in the Cassini radioscience experiment was implicitly postulated by Bertotti as having a pure general re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuovo Cimento
''Nuovo Cimento'' is a series of peer-reviewed scientific journals of physics. The series was first established in 1855, when Carlo Matteucci and Raffaele Piria started publishing ''Il Nuovo Cimento'' as the continuation of ''Il Cimento'', which they established in 1844. In 1897, it became the official journal of the Italian Physical Society. Over time, the journal split into several sub-journals: * ''Nuovo Cimento A'' (1965–1999): Focused on particle physics. The journal ended when it was merged into the ''European Physical Journal'', in 1999. * ''Nuovo Cimento B'' (1965–2010): Focused on relativity, astronomy, and mathematical physics. As of 1 January 2011 it continues publication as the ''European Physical Journal Plus''. * ''Nuovo Cimento C'' (1978–present): Focuses on geophysics, astrophysics, and biophysics. * ''Nuovo Cimento D'' (1982–1998): Focuses on solid state physics, atomic physics, and molecular biology. The journal ended when it was merged into the ''Europe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
