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The mass loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant $\Lambda\in\R$ was recently worked out, using the Newman-Penrose-Unti approach.
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There must be numerous exceptions, of course. For example, Penrose’s conformal treatment of spacetime does include a cosmological constant [ 46 ] . Also, Hawking studied gravitational radiation in an expanding universe, and in some setup which reduced to the Bondi mass for asymptotically flat spacetimes [ 47 ]
Cited in the paper.
Ref. [ 14 ] is an extension of Ref. [ 13 ] to include Maxwell fields. The case with purely Maxwell fields is clear: the mass-loss formula for electromagnetic (EM) radiation says that outgoing EM waves strictly decrease the total mass-energy of the source, whilst incoming EM waves from elsewhere strictly increase its total mass-energy. The gravitational case, on the other hand, is not as straightforward. See also Ref. [ 48 ] for a concise summary of the results found in Refs. [ 13 , 14 ]
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