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.