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v. t. e. The mathematics of general relativity is complicated. In Newton 's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone. In relativity, however, an object's length and the rate at which time ...
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.
v. t. e. 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. [1] The equations were published by Albert Einstein in 1915 in the form of a tensor equation [2] which related the local spacetime curvature (expressed by ...
e. General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal ...
If Einstein's system is defined as a combination of (1) the GPoR (by definition), (2) the PoE (for geometricalisation) and (3) SR (for continuity with previous theory). then we cannot very well lose either (1) or (2). This leaves open the possibility of eliminating (3), and losing full support for special relativity.
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
t. e. The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the (− + + +) metric signature, the gravitational part of the action is given as [1] where is the determinant of the metric tensor matrix, is the Ricci scalar, and is the Einstein ...
t. e. In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, [1] it was used by Albert Einstein to develop his general theory of relativity.