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The Meaning of Einstein's Equation — An explanation of Einstein's field equation, its derivation, and some of its consequences; Video Lecture on Einstein's Field Equations by MIT Physics Professor Edmund Bertschinger. Arch and scaffold: How Einstein found his field equations Physics Today November 2015, History of the Development of the Field ...
For a source right behind the lens, θ S = 0, the lens equation for a point mass gives a characteristic value for θ 1 that is called the Einstein angle, denoted θ E. When θ E is expressed in radians, and the lensing source is sufficiently far away, the Einstein Radius, denoted R E, is given by =. [2]
An Einstein Ring is a special case of gravitational lensing, caused by the exact alignment of the source, lens, and observer. This results in symmetry around the lens, causing a ring-like structure. [2] The geometry of a complete Einstein ring, as caused by a gravitational lens. The size of an Einstein ring is given by the Einstein radius.
Next, notice that only 10 of the original 14 equations are independent, because the continuity equation ; = is a consequence of Einstein's equations. This reflects the fact that the system is gauge invariant (in general, absent some symmetry, any choice of a curvilinear coordinate net on the same system would correspond to a numerically ...
Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise. Novel techniques developed by numerical relativity ...
Einstein discussed his idea with mathematician Marcel Grossmann and they concluded that general relativity could be formulated in the context of Riemannian geometry which had been developed in the 1800s. [10] In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and any momentum within it.
The core concept of general-relativistic model-building is that of a solution of Einstein's equations. Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold (usually defined by giving the metric in specific coordinates), and specific matter fields ...
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact 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.