ADM energy

Summary

The ADM energy is the total energy of an asymptotically flat initial data set in general relativity. It is defined by a flux integral of the metric over a large sphere at spatial infinity. Together with the ADM momentum it forms the ADM energy-momentum vector, whose Lorentzian length is the ADM mass. It arises as the boundary term that the Hamiltonian of the ADM formalism needs on an asymptotically flat slice. It is conserved in time, and by the positive mass theorem it is non-negative when the matter satisfies the dominant energy condition.