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Exact solutions in general relativity and Riemann curvature tensor

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

Difference between Exact solutions in general relativity and Riemann curvature tensor

Exact solutions in general relativity vs. Riemann curvature tensor

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 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.

Similarities between Exact solutions in general relativity and Riemann curvature tensor

Exact solutions in general relativity and Riemann curvature tensor have 7 things in common (in Unionpedia): Covariant derivative, Curvature form, General relativity, Pseudo-Riemannian manifold, Ricci curvature, Ricci decomposition, Tensor.

Covariant derivative

In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.

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Curvature form

In differential geometry, the curvature form describes the curvature of a connection on a principal bundle.

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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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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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Ricci decomposition

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.

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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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The list above answers the following questions

Exact solutions in general relativity and Riemann curvature tensor Comparison

Exact solutions in general relativity has 89 relations, while Riemann curvature tensor has 52. As they have in common 7, the Jaccard index is 4.96% = 7 / (89 + 52).

References

This article shows the relationship between Exact solutions in general relativity and Riemann curvature tensor. To access each article from which the information was extracted, please visit:

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