The Penrose property with a cosmological constant
Authors
Publication Date
2022-05-12Journal Title
Classical and Quantum Gravity
ISSN
0264-9381
Publisher
IOP Publishing
Volume
39
Issue
11
Language
en
Type
Article
This Version
VoR
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Cameron, P. (2022). The Penrose property with a cosmological constant. Classical and Quantum Gravity, 39 (11) https://doi.org/10.1088/1361-6382/ac66b7
Abstract
Abstract: A spacetime satisfies the non-timelike boundary version of the Penrose property if the timelike future of any point on I− contains the whole of I+ . This property was first discussed for asymptotically flat spacetimes by Penrose, along with an equivalent definition (the finite version). In this paper we consider the Penrose property in greater generality. In particular we consider spacetimes with a non-zero cosmological constant and we note that the two versions of the property are no longer equivalent. In asymptotically AdS spacetimes it is necessary to re-state the property in a way which is more suited to spacetimes with a timelike boundary. We arrive at a property previously considered by Gao and Wald. Curiously, this property was shown to fail in spacetimes which focus null geodesics. This is in contrast to our findings in asymptotically flat and asymptotically de Sitter spacetimes. We then move on to consider some further example spacetimes (with zero cosmological constant) which highlight features of the Penrose property not previously considered. We discuss spacetimes which are the product of a Lorentzian and a compact Riemannian manifold. Perhaps surprisingly, we find that both versions of the Penrose property are satisfied in this product spacetime if and only if they are satisfied in the Lorentzian spacetime only. We also discuss the Ellis–Bronnikov wormhole (an example of a spacetime with more than one asymptotically flat end) and the Hayward metric (an example of a non-singular black hole spacetime).
Keywords
Paper, general relativity, causality, conformal, cosmological constant, Penrose, spacetime, wormhole
Sponsorship
St John’s College, University of Cambridge (Todd/Goddard Fund)
Science and Technology Facilities Council (ST/P000681/1, ST/T000694/1)
Identifiers
cqgac66b7, ac66b7, cqg-108479.r4
External DOI: https://doi.org/10.1088/1361-6382/ac66b7
This record's URL: https://www.repository.cam.ac.uk/handle/1810/337129
Rights
Licence:
https://creativecommons.org/licenses/by/4.0/
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