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Exact solutions in general relativity and Ricci decomposition

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Exact solutions in general relativity and Ricci decomposition

Exact solutions in general relativity vs. Ricci decomposition

In general relativity, an exact solution is a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field. In semi-Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a pseudo-Riemannian manifold into pieces with useful individual algebraic properties.

Similarities between Exact solutions in general relativity and Ricci decomposition

Exact solutions in general relativity and Ricci decomposition have 11 things in common (in Unionpedia): Einstein field equations, Einstein tensor, General relativity, Gravitational wave, Petrov classification, Pseudo-Riemannian manifold, Ricci curvature, Riemann curvature tensor, Stress–energy tensor, Tensor, Weyl tensor.

Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

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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.

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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.

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Gravitational wave

Gravitational waves are the disturbance in the fabric ("curvature") of spacetime generated by accelerated masses and propagate as waves outward from their source at the speed of light.

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Petrov classification

In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.

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Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

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Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.

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Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.

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Stress–energy tensor

The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.

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Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

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Weyl tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold.

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The list above answers the following questions

Exact solutions in general relativity and Ricci decomposition Comparison

Exact solutions in general relativity has 89 relations, while Ricci decomposition has 35. As they have in common 11, the Jaccard index is 8.87% = 11 / (89 + 35).

References

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