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Metric tensor (general relativity)
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Metric tensor (general relativity) : ウィキペディア英語版
Metric tensor (general relativity)

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 time, distance, volume, curvature, angle, and separating the future and the past.
==Notation and conventions==

Throughout this article we work with a metric signature that is mostly positive (); see sign convention. The gravitation constant ''G'' will be kept explicit. The summation convention, where repeated indices are automatically summed over, is employed.

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