Smoothness of Compact Horizons

Larsson, Eric

doi:10.1007/s00023-014-0371-z

Cited by 13 publications

(9 citation statements)

References 27 publications

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“…14, was posted on the Archive (arXiv: 1406.5919) as the last of a series of three papers (the others being [58,59]). The very next day a related work by E. Larsson (arXiv:1406.6194 recently published in [54]), reaching similar conclusions on smoothness of Cauchy horizons and topology change, was also posted ( [54] mentions that it also appeared some days before on a public web repository of theses of the KTH Institute, Stockholm). This work and Larsson's follow quite different lines of proof.…”

Section: Acknowledgmentsmentioning

confidence: 93%

Area Theorem and Smoothness of Compact Cauchy Horizons

Minguzzi

2015

Commun. Math. Phys.

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We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.

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Section: Acknowledgmentsmentioning

confidence: 93%

Area Theorem and Smoothness of Compact Cauchy Horizons

Minguzzi

2015

Commun. Math. Phys.

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“…Some specific or technical topics of causality theory have not been discussed in this review. I give a list here pointing the reader to some literature -Chronology violation (time machines) and topology change (Geroch 1967;Tipler 1974Tipler , 1977Yodzis 1972Yodzis , 1973Galloway 1983bGalloway , 1995Kriele 1989;Hawking 1992;Ori 1993Ori , 2007Borde 1997Borde , 2004Krasnikov 1995Krasnikov , 2002Minguzzi 2015aMinguzzi , 2016aLarsson 2015;Lesourd 2018). -Spacetime boundaries (Penrose 1964(Penrose , 1965cSchmidt 1971a, b;Geroch et al 1972;Sachs 1973;Budic and Sachs 1974;Geroch 1977a;Szabados 1987Szabados , 1988Rácz 1987Rácz , 1988; Liang 1988, 1992;Scott and Szekeres 1994;Harris 1998Harris , 2000Harris , 2004Harris , 2017Marolf and Ross 2003;García-Parrado and Senovilla 2005;Low 2006;Flores 2007;Flores and Sánchez 2008;Flores and Harris 2007;Sánchez 2009;…”

Section: History and Peculiarities Of Causality Theorymentioning

confidence: 99%

Lorentzian causality theory

Minguzzi

2019

Living Rev Relativ

157

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I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results. I include complete proofs of some foundational results that are otherwise difficult to find in the literature (e.g. equivalence of some Lorentzian length definitions, upper semi-continuity of the length functional, corner regularization, etc.). The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory. It contains new results on classical concepts such as maximizing curves, achronal sets, edges, horismos, domains of dependence, Lorentzian distance. The treatment of causally pathological spacetimes requires the development of some new versatile causality notions, among which I found particularly convenient to introduce: biviability, chronal equivalence, araying sets, and causal versions of horismos and trapped sets. Their usefulness becomes apparent in the treatment of the classical singularity theorems, which is here considerably expanded in the exploration of some variations and alternatives.

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“…M \ C = I ∪ H, where H is a maximal globally hyperbolic spacetime with a compact and boundaryless Cauchy surface Σ. In this context C is a smooth [6], [8], [9], and totally geodesic null hypersurface, hence ruled by inextensible null geodesics called the null generators. We say that C is non-degenerate if there is at least one future or past incomplete generator (i.e.…”

Section: Introductionmentioning

confidence: 99%

A classification theorem for compact Cauchy horizons in vacuum spacetimes

Bustamante

Reiris

2021

Gen Relativ Gravit

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We establish a complete classification theorem for the topology and for the null generators of compact non-degenerate Cauchy horizons of time orientable smooth vacuum 3+1-spacetimes. We show that, either: (i) all generators are closed, or (ii) only two generators are closed and any other densely fills a two-torus, or (iii) every generator densely fills a two-torus, or (iv) every generator densely fills the horizon. We then show that, respectively to (i)-(iv), the horizon's manifold is either: (i') a Seifert manifold, or (ii') a lens space, or (iii') a two-torus bundle over a circle, or, (iv') a three-torus. All the four possibilities are known to arise in examples. In the last case, (iv), (iv'), we show in addition that the spacetime is indeed flat Kasner, thus settling a problem posed by Isenberg and Moncrief for ergodic horizons. The results of this article open the door for a full parameterization of the metrics of all vacuum spacetimes with a compact Cauchy horizon. The method of proof permits direct generalizations to higher dimensions.

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Smoothness of Compact Horizons

Cited by 13 publications

References 27 publications

Area Theorem and Smoothness of Compact Cauchy Horizons

Area Theorem and Smoothness of Compact Cauchy Horizons

Lorentzian causality theory

A classification theorem for compact Cauchy horizons in vacuum spacetimes

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