Einstein field equation

The Einstein field equation describes how space-time is curved by matter, and -the other way round- how matter is influenced by the curvature of space-time (i.e. how the curvature gives rise to gravity).

The field equation reads as follows:

where is the Ricci curvature tensor, is the Ricci curvature scalar, is the metric tensor, is the cosmological constant, is the stress-energy tensor, is pi, is the speed of light and is the gravitational constant which also occurs in Newton's law of gravity. describes the metric of the manifold and is a symmetric 4 x 4 tensor, so it has 10 independent components. Given the freedom of choice of the four spacetime coordinates, the independent equations reduce to 6.

These equations are the core of the mathematical formulation of General Relativity.