## ::Metric tensor (general relativity)

### ::concepts

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

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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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