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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.
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.
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows: = = (,) In the above, is the proper time of the path through spacetime, called the world-line, followed by the object velocity the above represents, and
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.
In contrast to all other modern theories of fundamental interactions, general relativity is a classical theory: it does not include the effects of quantum physics. The quest for a quantum version of general relativity addresses one of the most fundamental open questions in physics.
The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity" ( German : Relativitätstheorie ).
Numerical relativity, a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativity; Principle of relativity, used in Einstein's theories and derived from Galileo's principle; Theory of relativity, a general treatment that refers to both special relativity and general relativity