Note on positive-definiteness of the energy of the gravitational field
1960; Elsevier BV; Volume: 11; Issue: 1 Linguagem: Inglês
10.1016/0003-4916(60)90129-9
ISSN1096-035X
AutoresR. Arnowitt, S. Deser, Charles W. Misner,
Tópico(s)Geophysics and Gravity Measurements
ResumoThe energy of the gravitational field is shown to be positive-definite for the case where initially (a) the spatial metric gij can be made isotropic and (b) the second fundamental form Kij ≡ − (−g00)−12Γ0ij (which is essentially ∂gij∂t) is arbitrary apart from the coordinate condition K ≡ Kij3gij = 0 defining the initial t = const. surface. Physically, this situation corresponds to no wave excitations initially in gij, but arbitrary ones in Kij. 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 gij is also arbitrary initially) are discussed.
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