The variables used in general relativity to describe the shape of spacetime. If your question is about metric units, use the tag "units", and/or "si-units" if it is about the SI system specifically.
The variables used in general relativity to describe the geometry of spacetime. If your question is about metric units, use instead the tag units, and/or si-units if it is about the SI system specifically.
The metric tensor is a second rank (specifically, it is a (2,0) tensor) tensor $g$ with components $g_{\mu\nu}=g(\hat e_\mu,\hat e_\nu)\equiv\hat e_\mu\cdot\hat e_\nu$. It therefore describes distances and angles between vectors. Curvature tensors can be derived from it. All in all, it is arguably the most important concept in (pseudo-)Riemannian geometry, a subarea of differential-geometry.
This tensor is commonly used in general-relativity, where the curvature of spacetime describes the strength of gravity, in a sense. The Einstein Field Equation is a nonlinear system of differential equations for the metric tensor.
The metric tensor formulation of general relativity is a second-order formalism. The first-order formalism uses vielbeins, an approach known as the Tetrad formalism. See also Palatini Action.
