Metric tensor (general relativity)

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Flat spacetime Minkowski metric Special relativity Spherical coordinates Alcubierre metric

16 related topics

Local coordinates and matrix representations

Local coordinates Local patch One-form Gradients Tensor products

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Definition

Differentiable manifold Covariant Degree Symmetric tensor Nondegenerate

13 related topics

Curvature

Curvature Fundamental theorem of Riemannian geometry Connection Semi-Riemannian manifold Torsion

9 related topics

Topics to explore

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Overview

General relativity
Causal structure Causal spacetime structure
Spacetime
Gravitational potential
Schwarzschild metric
2-sphere
Gravitation constant
Mass
Here Deriving the Schwarzschild solution
Eddington–Finkelstein coordinates
Gullstrand–Painlevé coordinates
Kruskal–Szekeres coordinates
Lemaître coordinates
Reissner–Nordström metric
Kerr metric
Kerr–Newman metric

Notation and conventions

Definition

Differentiable manifold
Covariant Covariance and contravariance of vectors
Degree Tensor degree
Symmetric tensor
Nondegenerate Nondegenerate form
Signature Lorentz signature
Lorentzian manifold
Symmetric bilinear form
Tangent space
Dot product
Euclidean space
Positive definite Positive-definite bilinear form
Minkowski space

Local coordinates and matrix representations

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Nodes97

Edges96

Triples9

Avg. degree1.98

Density0.020619

Components1

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Important terminology

metric displaystyle tensor mu coordinates nu spacetime relativity local general matrix curvature given schwarzschild equations manifold space components ds interval

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
time	instance of	being used to define notions	0.80	text
distance	instance of	being used to define notions	0.80	text
volume	instance of	being used to define notions	0.80	text
curvature	instance of	being used to define notions	0.80	text
angle	instance of	being used to define notions	0.80	text
and separation of the future	instance of	being used to define notions	0.80	text
the past.In general relativity	instance of	being used to define notions	0.80	text
the metric tensor plays the role of the gravitational potential in the classical theory of gravitation	instance of	being used to define notions	0.80	text
although the physical content of the associated equations is entirely different	instance of	being used to define notions	0.80	text

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Local coordinates and matrix representations

Definition

Curvature

Key facts & relationships

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Overview

Notation and conventions

Definition

Local coordinates and matrix representations

Properties

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Volume

Curvature

Einstein's equations

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