The future is not always open

Grant, James D. E.; Kunzinger, Michael; Sämann, Clemens; Steinbauer, Roland

doi:10.1007/s11005-019-01213-8

Cited by 35 publications

(50 citation statements)

References 31 publications

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“…The latter reaches down to C 1,1 -at least as far as convexity and causality are concerned [16,13,14,5]. However, the Lipschitz property is decisive since it prevents the most dramatic downfalls in causality theory which are known to occur for Hölder continuous metrics [9,3,30,6,17]. More specifically, in the context of the initial value problem for the geodesic equation, the Lipschitz property guarantees the existence of solutions [35] which, due to the special geometry of the models at hand, are even (globally) unique [27].…”

Section: Introductionmentioning

confidence: 99%

Cut-and-paste for impulsive gravitational waves with Λ : The geometric picture

et al. 2019

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Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. Here we focus on non-expanding waves which later have been generalised to impulses travelling in all constantcurvature backgrounds, that is also the (anti-)de Sitter universe. While Penrose's original construction was based on his vivid geometric 'scissors-and-paste' approach in a flat background, until now a comparably powerful visualisation and understanding have been missing in the Λ = 0 case. In this work we provide such a picture: The (anti-)de Sitter hyperboloid is cut along the null wave surface, and the 'halves' are then re-attached with a suitable shift of their null generators across the wave surface. This special family of global null geodesics defines an appropriate comoving coordinate system, leading to the continuous form of the metric. Moreover, it provides a complete understanding of the nature of the Penrose junction conditions and their specific form. These findings shed light on recent discussions of the memory effect in impulsive waves.

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Section: Introductionmentioning

confidence: 99%

Cut-and-paste for impulsive gravitational waves with Λ : The geometric picture

et al. 2019

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“…While convexity fails below that regularity [26,43], nevertheless, most aspects of causality theory can be maintained even under Lipschitz regularity of the metric. Further below some significant changes occur [5,16], while some robust features continue to hold even in more general settings [2,15,27,35]. In particular, for C 1 -spacetimes, the push-up principle is still valid and I + (A) is open for any set A ⊆ M.…”

Section: Low Regularitymentioning

confidence: 97%

A note on the Gannon–Lee theorem

Schinnerl

Steinbauer

2021

Lett Math Phys

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We prove a Gannon–Lee theorem for non-globally hyperbolic Lorentzian metrics of regularity $$C^1$$ C 1 , the most general regularity class currently available in the context of the classical singularity theorems. Along the way, we also prove that any maximizing causal curve in a $$C^1$$ C 1 -spacetime is a geodesic and hence of $$C^2$$ C 2 -regularity.

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“…Hence γ is a timelike curve. Definition 2.5 Given a set S within an open neighborhood U , we define the causal future and timelike future of S within U as [9]). This is the main distinction between timelike curves and timelike almost everywhere curves.…”

Section: Proposition 24 Letmentioning

confidence: 99%