Einstein equations | Einstein gravitational 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 G_μν and T_μν, the actual number of equations reduces to 10, although there are an additional four differential identities (the Bianchi identities) satisfied by G_μν, one for each coordinate.

Bianchi identities | Einstein tensor | Ricci curvature tensor | scalar curvature