Einstein Field Equations

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.