A covariant formulation of the Landau-Lifshitz complex.

Details A covariant formulation of the Landau-Lifshitz complex. A covariant formulation of the Landau-Lifshitz complex.

Oct 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979gregr..11..233p&link_type=abstract

General Relativity and Gravitation, Volume 11, Issue 3, pp.233-243

Mathematics

8

Gravitation:Relativity

Scientific paper

For an asymptotically flat space-time (mathfrak{M} , g) with conformal completion, [Figure not available: see fulltext.]Ω2 g μν , the following theorem is proved: If h μv is any second-rank covariant tensor field on π such that (1) tilde g_{μ ν } = tilde h_{μ ν } on I +, where tilde h_{μ ν } = Ω ^2 h_{μ ν } , (2) the Riemann tensor of h μv is zero and (3) Ω ^{ - 2} tilde h^{μ ν } Ω left| {μ ^Ω } right|_ν = - 1 on J +, then the Landau-Lifshitz complex appropriately formulated from g μv and h μv gives a covariant definition of the total 4-momentum of the gravitational field equivalent to the Bondi prescription.

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