Total energy momentum in general relativity

The energy momentum of any asymptotically flat vacuum solution to the Einstein equations is a well-defined, conserved, Lorentz-covariant, timelike, future-pointing vector. The only requirement is that one be given asymptotically flat initial data that satisfy very weak continuity and falloff conditions; the three-metric must go flat faster than r−1/2. A large class of such data exists, consistent with the constraints, and the constraints play a key role in guaranteeing that the energy momentum is well behaved.