# 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.