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Einstein tensor

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Summary

The tensor Gμν=Rμν12RgμνG_{\mu\nu}=R_{\mu\nu}-\tfrac12 Rg_{\mu\nu}, whose covariant divergence vanishes.

Record metadata

Carrier(s)

Data

Axioms / constraints

Canonically induces

Concept sources

Incoming relations (arrows to this concept)

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Ricci curvature tensorEinstein tensor

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Combining Ricci and scalar curvature gives the Einstein tensor.

How to interpret this relation type

Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.

Relation sources

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Einstein tensorEinstein field equation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

The Einstein tensor, plus the cosmological term when included, forms the geometric side of Einstein’s equation.

How to interpret this relation type

A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.

Relation sources