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Exact solutions in general relativity and Ricci curvature

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

Difference between Exact solutions in general relativity and Ricci curvature

Exact solutions in general relativity vs. Ricci curvature

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 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.

Similarities between Exact solutions in general relativity and Ricci curvature

Exact solutions in general relativity and Ricci curvature have 9 things in common (in Unionpedia): Cambridge University Press, Cosmological constant, Curvature form, Einstein field equations, General relativity, Heat equation, Pseudo-Riemannian manifold, Ricci decomposition, Riemann curvature tensor.

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Cosmological constant

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space.

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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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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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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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Heat equation

The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.

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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 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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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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The list above answers the following questions

Exact solutions in general relativity and Ricci curvature Comparison

Exact solutions in general relativity has 89 relations, while Ricci curvature has 84. As they have in common 9, the Jaccard index is 5.20% = 9 / (89 + 84).

References

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

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