Causal simplicity and (maximal) null pseudoconvexity

Hedicke, Jakob; Minguzzi, E.; Schinnerl, Benedict; Steinbauer, Roland; Suhr, Stefan

doi:10.1088/1361-6382/ac2be1

Cited by 5 publications

(3 citation statements)

References 18 publications

(17 reference statements)

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“…As part of that goal, Penrose has pioneered various theories that have been remarkably successful for their achievements and originality, for instance, the study of causal relations [27,59], in the sense of describing the global properties of spacetime depending on what events influence to (or are influenced by) others. Most of the tools used in this field are quite simple, but the idea is powerful enough so that it has been very fruitful and still remains active today [1,14,33]. Non-spacelike curves are one of these tools, so if we would want to characterize the causality in any geometrical new model of the spacetime, then it will be necessary to describe such curves.…”

Section: Introductionmentioning

confidence: 99%

The space of light rays: Causality and L–boundary

Bautista

Ibort

Lafuente³

2022

Gen Relativ Gravit

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The space of light rays $${\mathcal {N}}$$ N of a conformal Lorentz manifold $$(M,{\mathcal {C}})$$ ( M , C ) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold $${\mathcal {N}}$$ N , strongly inspired on R. Penrose’s twistor theory, keeps all information of M and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of $${\mathcal {N}}$$ N , such as the space of skies $$\varSigma $$ Σ and the contact structure $${\mathcal {H}}$$ H , are introduced. The causal structure of M is characterized as part of the geometry of $${\mathcal {N}}$$ N . A new causal boundary for spacetimes M prompted by R. Low, the L-boundary, is constructed in the case of 3–dimensional manifolds M and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of $${\mathcal {N}}$$ N and not on the geometry of the spacetime M. The properties satisfied by the L–boundary $$\partial M$$ ∂ M permit to characterize the obtained extension $${\overline{M}}=M\cup \partial M$$ M ¯ = M ∪ ∂ M and this characterization is also proposed for general dimension.

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Section: Introductionmentioning

confidence: 99%

The space of light rays: Causality and L–boundary

Bautista

Ibort

Lafuente³

2022

Gen Relativ Gravit

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“…In [18] it is shown that causal geodesics in static spacetimes are maximising if and only if their Riemannian parts are minimizing and so one can easily construct both maximising timelike and null geodesics that branch. Lemma 3.3.…”

Section: Branchingmentioning

confidence: 99%

The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics

Kunzinger,

Ohanyan,

Schinnerl

et al. 2021

Preprint

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We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity C 1 . For metrics of such low regularity, two main obstacles have to be addressed. On the one hand, the Ricci tensor now is distributional, and on the other hand, unique solvability of the geodesic equation is lost. To deal with the first issue in a consistent way, we develop a theory of tensor distributions of finite order, which also provides a framework for the recent proofs of the theorems of Hawking and of Penrose for C 1 -metrics [7]. For the second issue, we study geodesic branching and add a further alternative to causal geodesic incompleteness to the theorem, namely a condition of maximal causal non-branching. The genericity condition is re-cast in a distributional form that applies to the current reduced regularity while still being fully compatible with the smooth and C 1,1 -settings. In addition, we develop refinements of the comparison techniques used in the proof of the C 1,1 -version of the theorem [8]. The necessary results from low regularity causality theory are collected in an appendix.

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“…As part of that goal, Penrose has pioneered various theories that have been remarkably successful for their achievements and originality, for instance, the study of causal relations [27], [59], in the sense of describing the global properties of spacetime depending on what events influence to (or are influenced by) others. Most of the tools used in this field are quite simple, but the idea is powerful enough so that it has been very fruitful and still remains active today [1], [33], [14]. Non-spacelike curves are one of these tools, so if we would want to characterize the causality in any geometrical new model of the spacetime, then it will be necessary to describe such curves.…”

Section: Introductionmentioning

confidence: 99%

The space of light rays: Causality and $L$-boundary

Bautista,

Ibort,

Lafuente

2022

Preprint

View full text Add to dashboard Cite

The space of light rays N of a conformal Lorentz manifold (M, C) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold N , strongly inspired on R. Penrose's twistor theory, keeps all information of M and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of N , such as the space of skies Σ and the contact structure H, are introduced. The causal structure of M is characterized as part of the geometry of N . A new causal boundary for spacetimes M prompted by R. Low, the L-boundary, is constructed in the case of 3-dimensional manifolds M and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of N and not on the geometry of the spacetime M . The properties satisfied by the L-boundary ∂M permit to characterize the obtained extension M = M ∪ ∂M and this characterization is also proposed for general dimension.

show abstract

Causal simplicity and (maximal) null pseudoconvexity

Cited by 5 publications

References 18 publications

The space of light rays: Causality and L–boundary

The space of light rays: Causality and L–boundary

The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics

The space of light rays: Causality and $L$-boundary

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