Metric tensor (general relativity)

${\displaystyle {\begin{pmatrix}g_{00}&g_{01}&g_{02}&g_{03}\\g_{10}&g_{11}&g_{12}&g_{13}\\g_{20}&g_{21}&g_{22}&g_{23}\\g_{30}&g_{31}&g_{32}&g_{33}\\\end{pmatrix}}}$ Metric tensor of spacetime in general relativity written as a matrix

In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.

In general relativity, the metric tensor plays the role of the gravitational potential in the classical theory of gravitation, although the physical content of the associated equations is entirely different.^[1] Gutfreund and Renn say "that in general relativity the gravitational potential is represented by the metric tensor."^[2]