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Mathematics of general relativity information


When studying and formulating Albert Einstein's theory of general relativity, various mathematical structures and techniques are utilized. The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics of general relativity.

Note: General relativity articles using tensors will use the abstract index notation.

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Mathematics of general relativity

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theory of general relativity, various mathematical structures and techniques are utilized. The main tools used in this geometrical theory of gravitation...

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Introduction to the mathematics of general relativity

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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...

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General relativity

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General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published...

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The Meaning of Relativity

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overview of his theory of relativity and is his only book that provides an accessible overview of the physics and mathematics of general relativity. Einstein...

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Introduction to general relativity

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General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed...

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Variational methods in general relativity

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general relativity refers to various mathematical techniques that employ the use of variational calculus in Einstein's theory of general relativity....

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Principle of relativity

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framework of special relativity the Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell...

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Tensor calculus

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electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory...

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Cauchy surface

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physics of general relativity, a Cauchy surface is usually interpreted as defining an "instant of time". In the mathematics of general relativity, Cauchy...

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Physical theories modified by general relativity

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between general relativity and classical mechanics, and shares many attributes with classical mechanics. In the following discussion, the mathematics of general...

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Spacetime topology

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topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional...

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General Relativity and Gravitation

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general relativity, gravity, supergravity, quantum gravity, string theory (including extensions), relativity, and the related complex mathematics involved...

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Tests of general relativity

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Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein...

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Numerical relativity

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Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end...

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Einstein field equations

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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...

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History of general relativity

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General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915...

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Geodesics in general relativity

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In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from...

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List of mathematical topics in relativity

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This is a list of mathematical topics in relativity, by Wikipedia page. Foundational issues principle of relativity speed of light faster-than-light biquaternion...

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Lovelock theory of gravity

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Lovelock's theory of gravity (often referred to as Lovelock gravity) is a generalization of Einstein's theory of general relativity introduced by David...

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Bernhard Riemann

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laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time. Riemann was...

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Theory of relativity

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The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed...

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Solving the geodesic equations

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equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining...

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List of mathematical physics journals

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Communications in Mathematical Physics General Relativity and Gravitation International Journal of Geometric Methods in Modern Physics Journal of Geometry and...

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General relativity priority dispute

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Einstein's discovery of the gravitational field equations of general relativity and David Hilbert's almost simultaneous derivation of the theory using an...

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Alternatives to general relativity

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to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory of general relativity...

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