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We present the asymptotic solutions for spacetimes with non-zero cosmological constant $\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism.
doi: http://dx.doi.org/10.1016/0003-4916(60)90021-X
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URL http://stacks.iop.org/0264-9381/32/i=20/a=205011
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The cosmological constant is well, a constant. In the Newman-Penrose formalism, the peeling property can be shown by assuming Ψ 0 = O ( r − 5 ) \Psi_{0}=O(r^{-5}) and using the Bianchi identities. This was worked out for the asymptotically flat case in Ref. [ 2 ] . What appears in the Bianchi identities involving the Ricci scalar (which is proportional to the cosmological constant) are only its derivatives, not itself — which are all zero since it is a constant. Thus, one still arrives at the peeling property with a cosmological constant present, as it has no effect on the Bianchi identities [ 12 ] . A different proof involving the use of spinors for the peeling property of (weakly) asymptotically simple spacetimes (which include asymptotically de Sitter spacetimes) may be found in Section 9.7 of Ref. [ 4 ]
Cited in the paper.
We should clarify that when we say “Szabados-Tod null tetrad”, we are referring to a null tetrad comprising their \mathaccentV v e c 17 E l \mathaccentV{vec}17E{l} and \mathaccentV v e c 17 E n \mathaccentV{vec}17E{n} , whilst retaining Newman-Unti’s \mathaccentV v e c 17 E m \mathaccentV{vec}17E{m} and \mathaccentV v e c 17 E \mathaccentV b a r 016 m \mathaccentV{vec}17E{\mathaccentV{bar}016{m}} . This will be defined explicitly in Section 2
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URL http://stacks.iop.org/0264-9381/33/i=14/a=145006
E.T. Newman, Classical and Quantum Gravity 33 · 2016
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V.-L. Saw, “Mass-loss due to gravitational waves with Λ > 0 \Lambda>0 ”, Proceedings from the Conference on Cosmology, Gravitational Waves and Particles, 6th to 10th of February, 2017, held at the Institute of Advanced Studies, Nanyang Technological University, Singapore (World Scientific). (In preparation.) (2017)
2017
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