## ::Metric tensor (general relativity)

### ::concepts

Metric::partial    Tensor::general    Space::sigma    Local::where    Matrix::''m''    Given::manifold

{{#invoke:Hatnote|hatnote}} {{#invoke:Infobox|infobox}} In general relativity, the metric tensor (or simply, the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential familiar from Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past.

Notation and conventions: Throughout this article we work with a metric signature that is mostly positive (− + + +); see sign convention. As is customary in relativity, units are used where the speed of light c = 1. The gravitation constant G will be kept explicit. The summation convention, where repeated indices are automatically summed over, is employed.

Metric tensor (general relativity) sections
Intro  Definition  Local coordinates and matrix representations  Examples   Volume   Curvature  Einstein's equations   See also   References  External links

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