Dominant Energy Condition

The dominant energy condition on an initial data set requires its scalar energy density and momentum covector to satisfy

Thus the energy density is nonnegative and dominates the momentum density pointwise. The densities must be defined using one consistent normalization of the Einstein constraint equations. When the cosmological constant is zero and , this condition reduces to nonnegative scalar curvature of the Riemannian metric. In charged data the corresponding matter condition subtracts the electromagnetic energy and momentum before taking the norm.