60 relations: Aichelburg–Sexl ultraboost, Alcubierre drive, Anti-de Sitter space, Anti-gravity, Arthur Geoffrey Walker, Asymptotically flat spacetime, BKL singularity, Bonnor beam, BTZ black hole, C. V. Vishveshwara, Causal loop, Chronology protection conjecture, Closed timelike curve, Congruence (general relativity), Congruence (manifolds), Cornelius Lanczos, Dust solution, Einstein field equations, Electrovacuum solution, Energy condition, Fluid solution, Frame fields in general relativity, Friedmann–Lemaître–Robertson–Walker metric, Gödel metric, General relativity, George Barker Jeffery, GRTensorII, Index of physics articles (E), Interior Schwarzschild metric, Introduction to general relativity, James M. Bardeen, Jürgen Ehlers, Jean-Pierre Petit, Karl Schwarzschild, Kasner metric, Kerr metric, Kerr–Newman metric, Lambdavacuum solution, Linearized gravity, Mathematics of general relativity, Monochromatic electromagnetic plane wave, Newton's identities, Newton–Cartan theory, Non-exact solutions in general relativity, Null dust solution, Petrov classification, Raychaudhuri equation, Retrocausality, Roy Kerr, Scalar field solution, ..., Schwarzschild metric, Segre classification, Solutions of the Einstein field equations, Symmetry (physics), Taub–NUT space, Theoretical motivation for general relativity, Time travel, Vacuum solution (general relativity), Warped geometry, White–Juday warp-field interferometer. Expand index (10 more) »
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.
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Alcubierre drive
The Alcubierre drive or Alcubierre warp drive (or Alcubierre metric, referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.
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Anti-de Sitter space
In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.
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Anti-gravity
Anti-gravity (also known as non-gravitational field) is an idea of creating a place or object that is free from the force of gravity.
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Arthur Geoffrey Walker
Arthur Geoffrey Walker (17 July 1909 in Watford, Hertfordshire, England – 31 March 2001) was a leading mathematician who made important contributions to physics and physical cosmology.
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Asymptotically flat spacetime
An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime.
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BKL singularity
A Belinsky-Khalatnikov-Lifshitz (BKL) singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by an anisotropic, homogeneous, chaotic solution to Einstein's field equations of gravitation.
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Bonnor beam
In general relativity, the Bonnor beam is an exact solution which models an infinitely long, straight beam of light.
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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.
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C. V. Vishveshwara
C.
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Causal loop
A causal loop in the context of time travel or the causal structure of spacetime, is a sequence of events (actions, information, objects, people) in which an event is among the causes of another event, which in turn is among the causes of the first-mentioned event.
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Chronology protection conjecture
The chronology protection conjecture is a conjecture first proposed by Stephen Hawking which hypothesizes that the laws of physics are such as to prevent time travel on all but submicroscopic scales.
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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.
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Congruence (general relativity)
In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime.
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Congruence (manifolds)
In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold.
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Cornelius Lanczos
Cornelius (Cornel) Lanczos (Lánczos Kornél,, born as Kornél Lőwy, until 1906: Löwy (Lőwy) Kornél) was a Jewish Hungarian mathematician and physicist, who was born on February 2, 1893, and died on June 25, 1974.
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Dust solution
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure.
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Einstein field equations
The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.
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Electrovacuum solution
In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass-energy present is the field energy of an electromagnetic field, which must satisfy the (curved-spacetime) source-free Maxwell equations appropriate to the given geometry.
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Energy condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is one of various alternative conditions which can be applied to the matter content of the theory, when it is either not possible or desirable to specify this content explicitly.
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Fluid solution
In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid.
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Frame fields in general relativity
In general relativity, a frame field (also called a tetrad or vierbein) is a set of four orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime.
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Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding or contracting universe that is path connected, but not necessarily simply connected.
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Gödel metric
The Gödel metric is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution).
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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George Barker Jeffery
George Barker Jeffery FRS(9 May 1891 – 27 April 1957) was a leading mathematical physicist in the early twentieth century.
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GRTensorII
GRTensorII is a Maple package designed for tensor computations, particularly in general relativity.
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Index of physics articles (E)
The index of physics articles is split into multiple pages due to its size.
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Interior Schwarzschild metric
In Einstein's theory of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid (implying that density is constant throughout the body) and has zero pressure at the surface.
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Introduction to general relativity
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915.
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James M. Bardeen
James Maxwell Bardeen (born May 9, 1939) is an American physicist, well known for his work in general relativity, particularly his role in formulating the laws of black hole mechanics. He also discovered the Bardeen vacuum, an exact solution of the Einstein field equation.
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Jürgen Ehlers
Jürgen Ehlers (29 December 1929 – 20 May 2008) was a German physicist who contributed to the understanding of Albert Einstein's theory of general relativity.
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Jean-Pierre Petit
Jean-Pierre Petit (born 5 April 1937, Choisy-le-Roi) is a French scientist, senior researcher at National Center for Scientific Research (CNRS) as an astrophysicist in Marseille Observatory, now retired.
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Karl Schwarzschild
Karl Schwarzschild (October 9, 1873 – May 11, 1916) was a German physicist and astronomer.
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Kasner metric
The Kasner metric (developed by and named for the American mathematician Edward Kasner in 1921) is an exact solution to Einstein's theory of general relativity.
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Kerr metric
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical event horizon.
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Kerr–Newman metric
The Kerr–Newman metric is a solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding a charged, rotating mass.
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Lambdavacuum solution
In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term.
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Linearized gravity
Linearized gravity is an approximation scheme in general relativity in which the nonlinear contributions from the spacetime metric are ignored, simplifying the study of many problems while still producing useful approximate results.
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Mathematics of general relativity
The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying and formulating Albert Einstein's theory of general relativity.
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Monochromatic electromagnetic plane wave
In general relativity, the monochromatic electromagnetic plane wave spacetime is the analog of the monochromatic plane waves known from Maxwell's theory.
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Newton's identities
In mathematics, Newton's identities, also known as the Newton–Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials.
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Newton–Cartan theory
Newton–Cartan theory (or geometrized Newtonian gravitation) is a geometrical re-formulation, as well as a generalization, of Newtonian gravity first introduced by Élie Cartan and Kurt Friedrichs and later developed by Dautcourt, Dixon, Dombrowski and Horneffer, Ehlers, Havas, Künzle, Lottermoser, Trautman, and others.
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Non-exact solutions in general relativity
Non-exact solutions in general relativity are solutions of Albert Einstein's field equations of general relativity which hold only approximately.
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Null dust solution
In mathematical physics, a null dust solution (sometimes called a null fluid) is a Lorentzian manifold in which the Einstein tensor is null.
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Petrov classification
In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.
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Raychaudhuri equation
In general relativity, the Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter.
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Retrocausality
Retrocausality or Backwards causation is a concept of cause and effect where the effect precedes its cause in time.
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Roy Kerr
Roy Patrick Kerr (born 16 May 1934) is a New Zealand mathematician who discovered the Kerr geometry, an exact solution to the Einstein field equation of general relativity.
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Scalar field solution
In general relativity, a scalar field solution is an exact solution of the Einstein field equation in which the gravitational field is due entirely to the field energy and momentum of a scalar field.
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Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the 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.
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Segre classification
The Segre classification is an algebraic classification of rank two symmetric tensors.
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Solutions of the Einstein field equations
Solutions of the Einstein field equations are spacetimes that result from solving the Einstein field equations (EFE) of general relativity.
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Symmetry (physics)
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.
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Taub–NUT space
The Taub–NUT metric is an exact solution to Einstein's equations.
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Theoretical motivation for general relativity
A theoretical motivation for general relativity, including the motivation for the geodesic equation and the Einstein field equation, can be obtained from special relativity by examining the dynamics of particles in circular orbits about the earth.
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Time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically using a hypothetical device known as a time machine.
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Vacuum solution (general relativity)
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.
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Warped geometry
In mathematics and physics, in particular differential geometry and general relativity, a warped geometry is a Riemannian or Lorentzian manifold whose metric tensor can be written in form The geometry almost decomposes into a Cartesian product of the y geometry and the x geometry – except that the x part is warped, i.e. it is rescaled by a scalar function of the other coordinates y. For this reason, the metric of a warped geometry is often called a warped product metric.
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White–Juday warp-field interferometer
The White–Juday warp-field interferometer is an experiment designed to detect a microscopic instance of a warping of spacetime.
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Redirects here:
Exact solution (general relativity), Exact solutions of Einstein's field equations.
References
[1] https://en.wikipedia.org/wiki/Exact_solutions_in_general_relativity