2022
DOI: 10.1088/1361-6382/ac395b
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Asymptotic structure with a positive cosmological constant

Abstract: This is the second of two papers that study the asymptotic structure of space-times with a non-negative cosmological constant Λ. This paper deals with the case Λ>0. Our approach is founded on the `tidal energies' built with the Weyl curvature and, specifically, we use the asymptotic super-Poynting vector computed from the rescaled Bel-Robinson tensor at infinity to provide a covariant, gauge-invariant, criterion for the existence, or absence, of gravitational radiation at infinity. The fundamental idea we p… Show more

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Cited by 19 publications
(77 citation statements)
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References 82 publications
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“…More importantly, we have argued that the criterion is equivalent to the standard one -based on the news tensor-for the Λ = 0 case. Adding appropriate structure on (J , h ab , D ab ) which allows to deal with 'incoming and outgoing' waves, we are developing a framework [45] in order to recover further properties of the asymptotically flat case. In particular, ways to define asymptotic symmetries at infinity, as well as enlightening evidences for the existence of news-like tensor fields on J in the presence of a positive cosmological constant, emerge.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…More importantly, we have argued that the criterion is equivalent to the standard one -based on the news tensor-for the Λ = 0 case. Adding appropriate structure on (J , h ab , D ab ) which allows to deal with 'incoming and outgoing' waves, we are developing a framework [45] in order to recover further properties of the asymptotically flat case. In particular, ways to define asymptotic symmetries at infinity, as well as enlightening evidences for the existence of news-like tensor fields on J in the presence of a positive cosmological constant, emerge.…”
Section: Discussionmentioning
confidence: 99%
“…There exists one proposal [41] that requires knowledge of the physical spacetime, but we aim at handling this problem using information solely from, or on top of, J + . A worth-exploring possibility arising naturally in our scheme is partly related to the algebraic structure of the rescaled Weyl tensor in relation with N α [45]. In any case, when Λ > 0 it seems necessary to endow (J + , h ab , D ab ) with further structure, essentially a distinguished or chosen congruence of curves which depends on the physical properties of the spacetime under consideration (see also [46]).…”
Section: Comparison With the Asymptotically Flat Case (λ = 0)mentioning
confidence: 99%
“…The analysis of the asymptotic structure of general relativity has also been extended to spacetimes which are asymptotically (A)dS 4 [63][64][65][66][67][68][69], where part of the motivations and intriguing questions pertain to the very nature, when Λ = 0, of gravitational radiation, mass, angular momentum, and news [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85]. Even if there is no notion of S-matrix in this context, there are meaningful asymptotic symmetries and (yet poorly understood) memory effects.…”
Section: Motivationsmentioning
confidence: 99%
“…The notion of radiation for spacetimes with Λ = 0 is poorly understood [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85]. Although here we have not directly discussed notions pertaining to gravitational waves and quadrupole formulas in (A)dS, we have seen how certain well-defined quantities in asymptotically flat spacetimes generalize to the case Λ = 0 and ∂ u q AB = 0 (the question of whether these remain the relevant quantities is however open).…”
Section: • Logarithmic Termsmentioning
confidence: 99%
“…The problem of the existence of news-like objects in this case, and the question of in-and out-going radiation are discussed in section 5 and the existence of asymptotic symmetries is studied in section 6. I end the paper with a list of examples presented in [32,31] and some closing comments.…”
Section: Introductionmentioning
confidence: 99%