What is the name of the equations which are a set of partial differential equations produced by Einstein relating to the description of gravity as a geometric property of space and time which went on to replace Isaac Newton's rotating spheres argument which attempts to define that true rotational motion can be defined by observing the tension in the string joining two identical spheres?
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Rotating spheres Isaac Newton's rotating spheres argument attempts to demonstrate that true rotational motion can be defined by observing the tension in the string joining two identical spheres. The basis of the argument is that all observers make two observations: the tension in the string joining the bodies (which is the same for all observers) and the rate of rotation of the spheres (which is different for observers with differing rates of rotation). Only for the truly non-rotating observer will the tension in the string be explained using only the observed rate of rotation. For all other observers a "correction" is required (a centrifugal force) that accounts for the tension calculated being different from the one expected using the observed rate of rotation. It is one of five arguments from the "properties, causes, and effects" of true motion and rest that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to "what"?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.
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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. General relativity is considered probably the most beautiful of all existing physical theories. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or 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 partial differential equations.
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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. These solutions are typically found by treating the gravitational field, formula_1, as a background space-time, formula_2, (which is usually an exact solution) plus some small perturbation, formula_3. Then one is able to solve the Einstein field equations as a series in formula_3, dropping higher order terms for simplicity.
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Sticky bead argument In general relativity, the sticky bead argument is a simple thought experiment designed to show that gravitational radiation is indeed predicted by general relativity, and can have physical effects. These claims were not widely accepted prior to about 1955, but after the introduction of the bead argument, any remaining doubts soon disappeared from the research literature.
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Jacobi ellipsoid A Jacobi ellipsoid is an oblate ellipsoid under equilibrium which arises when a self-gravitating fluid body of uniform density rotates with a constant angular velocity. It is named after the German mathematician Carl Gustav Jacob Jacobi.
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Einstein–Rosen metric The Einstein–Rosen metric is an exact solution of Einstein's field equation. It was derived by Albert Einstein and Nathan Rosen in 1937. It is the first exact solution of Einstein's equation that described the propagation of a gravitational wave.
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Vasiliev Equations Vasiliev Equations are "formally" consistent gauge invariant nonlinear equations whose linearization over a specific vacuum solution describes free massless higher-spin fields on anti-de Sitter space. The Vasiliev equations are classical equations and no Lagrangian is known that starts from canonical two-derivative Fronsdal Lagrangian and is completed by interactions terms. There is a number of variations of Vasiliev equations that work in three, four and arbitrary number of space-time dimensions. Vasiliev's equations admit supersymmetric extensions with any number of super-symmetries and allow for Yang-Mills gaugings. Vasiliev's equations are background independent, the simplest exact solution being anti-de Sitter space. It is important to note that locality is not properly implemented and the equations give a solution of certain formal deformation procedure, which is difficult to map to field theory language. The higher-spin AdS/CFT correspondence is reviewed in Higher-Spin Gauge Theory article.
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Einstein aether theory In physics the Einstein æther theory, also called æ-theory, is a generally covariant modification of general relativity which describes a spacetime endowed with both a metric and a unit timelike vector field named the æther. The theory has a preferred reference frame and hence violates Lorentz invariance.
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Ricci scalars (Newman–Penrose formalism) In the Newman–Penrose (NP) formalism of general relativity, independent components of the Ricci tensors of a four-dimensional spacetime are encoded into seven (or ten) Ricci scalars which consist of three real scalars formula_1, three (or six) complex scalars formula_2 and the NP curvature scalar formula_3. Physically, Ricci-NP scalars are related with the energy–momentum distribution of the spacetime due to Einstein's field equation.
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History of general relativity General relativity (GR) is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.
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Van Stockum dust In general relativity, the van Stockum dust is an exact solution of the Einstein field equation in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is "increasing" with distance from this axis, the solution is rather artificial, but as one of the simplest known solutions in general relativity, it stands as a pedagogically important example.
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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. Solving the field equations actually gives a Lorentz manifold. Solutions are broadly classed as "exact" or "non-exact".
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Bogomolny equations In mathematics, the Bogomolny equations for magnetic monopoles are the equations "F" = *"D""φ", where "F" is the curvature of a connection "A" on a "G"-bundle over a 3-manifold "M", "φ" is a section of the corresponding adjoint bundle and * is the Hodge star operator on "M". These equations are named after E. B. Bogomolny.
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Clairaut's theorem Clairaut's theorem is a general mathematical law giving the surface gravity on a viscous rotating ellipsoid in equilibrium under the action of its gravitational field and centrifugal force. It was published in 1743 by Alexis Claude Clairaut in his "Théorie de la figure de la terre, tirée des principes de l'hydrostatique" ("Theory of the shape of the earth, drawn from the principles of hydrostatics") which synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid. It was initially used to relate the gravity at any point on the Earth's surface to the position of that point, allowing the ellipticity of the Earth to be calculated from measurements of gravity at different latitudes. Today it has been largely supplanted by the Somigliana equation.
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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. In this re-formulation, the structural similarities between Newton's theory and Albert Einstein's general theory of relativity are readily seen, and it has been used by Cartan and Friedrichs to give a rigorous formulation of the way in which Newtonian gravity can be seen as a specific limit of general relativity, and by Jürgen Ehlers to extend this correspondence to specific solutions of general relativity.
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Post-Newtonian expansion Post-Newtonian expansions in general relativity 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.
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Einstein tensor In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner consistent with energy and momentum conservation.
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Riemannian Penrose inequality In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The Riemannian Penrose inequality is an important special case. Specifically, if ("M", "g") is an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and ADM mass "m", and "A" is the area of the outermost minimal surface (possibly with multiple connected components), then the Riemannian Penrose inequality asserts
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Spherical pendulum In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass "m" moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity.
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Wahlquist fluid In general relativity, the Wahlquist fluid is an exact rotating perfect fluid solution to Einstein's equation with equation of state corresponding to constant gravitational mass density.
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CGh physics "cGh" physics refers to the mainstream attempts in physics to unify relativity, gravitation and quantum mechanics, in particular following the ideas of Matvei Petrovich Bronstein and George Gamow. The letters are the standard symbols for the speed of light ("c"), the gravitational constant ("G"), and Planck's constant ("h").
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Higher-dimensional Einstein gravity Higher-dimensional Einstein gravity is any of various physical theories that attempt to generalise to higher dimensions various results of the well established theory of standard (four-dimensional) Einstein gravity, that is, general relativity. This attempt at generalisation has been strongly influenced in recent decades by string theory.