Note on positive-definiteness of the energy of the gravitational field

The energy of the gravitational field is shown to be positive-definite for the case where initially (a) the spatial metric g_(ij) can be made isotropic and (b) the second fundamental form K_(ij) ≡ -(-g^(00)^(-12)Γ^0_(ij) (which is essentially ) is arbitrary apart from the coordinate condition K ≡ K_(ij)^3g_(ij) = 0 defining the initial t = const. surface. Physically, this situation corresponds to no wave excitations initially in g_(ij), but arbitrary ones in K_(ij). More precisely, the two canonical coordinates of the field are initially zero, while their conjugate momenta are arbitrary. The total energy of the system is also positive when sources with positive energies are coupled to the gravitational field. Some aspects of the general problem (where g_(ij) is also arbitrary initially) are discussed