A new class of compact spacetimes without closed causal geodesics

Guediri, Mohammed

doi:10.1007/s10711-007-9131-2

Cited by 3 publications

(2 citation statements)

References 12 publications

(9 reference statements)

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“…They have some interesting mathematical peculiarities. The reader is referred to the works by Tipler (1979), Galloway (1984Galloway ( , 1986a, Guediri (2002Guediri ( , 2003Guediri ( , 2007, Romero and Sánchez (1995), Sánchez (1997Sánchez ( , 2006 and references therein.…”

Section: Time Orientationmentioning

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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Section: Time Orientationmentioning

confidence: 99%

Lorentzian causality theory

Minguzzi

2019

Living Rev Relativ

157

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“…More recently, Guediri has proved that compact flat spacetimes contain a causal periodic geodesic [14], and that such spacetimes contain a periodic timelike geodesic if and only if the fundamental group of the underlying manifold contains a nontrivial timelike translation [15]. Non existence results for periodic causal geodesics are also available, see [12,16,17].…”

Section: Introductionmentioning

confidence: 99%

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

2009

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ABSTRACT. We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is never vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a never vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

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A criterion for global hyperbolicity of left-invariant Lorentz metrics on Lie groups

Guediri

2008

Journal of Geometry and Physics

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A new class of compact spacetimes without closed causal geodesics

Abstract: We construct the first examples of geodesically complete compact spacetimes admitting a regular globally hyperbolic covering, but which do not contain closed causal geodesics.

Cited by 3 publications

References 12 publications

Lorentzian causality theory

Lorentzian causality theory

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

A criterion for global hyperbolicity of left-invariant Lorentz metrics on Lie groups

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