The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that
describe the gravitational effects produced by a given mass in general relativity.
As result of the symmetry of 
and 
, the actual number of equations reduces to 10, although
there are an additional four differential identities (the Bianchi
identities) satisfied by 
, one for each coordinate.
The Einstein field equations state that
 |
where 
is the stress-energy tensor, and
 |
is the Einstein tensor, with 
the Ricci curvature
tensor and 
the scalar curvature.
The opening sequence of the 2003 French film Les Triplettes de Belleville (The Triplets of Belleville) features the Einstein field equations.
