Aspects of $$C^0$$ causal theory

Ling, Eric

doi:10.1007/s10714-020-02708-9

Cited by 19 publications

(21 citation statements)

References 21 publications

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“…The following result is known as the push-up property which is proved in [8,Theorem 4.5]. See also [2,Lemma 1.15] Proposition A.2 [2,8]. Let (M, g) be a Lipschitz spacetime.…”

Section: B Asymptotics: a Class Of Examplesmentioning

confidence: 97%

“…We first prove (1). Note first that J + (p, M ) cannot contain all of J 2 (as otherwise a past inextendible portion of J 2 would be imprisoned in a compact set which contradicts strong causality [8,Proposition 3.3]). Together with J + (p, M ) ∩ J 2 = ∅, this implies that there exists a point q ∈ ∂J + (p, M ) ∩ J 2 .…”

Section: Next We Consider Examples Of the Following Typementioning

confidence: 99%

“…Since we are working with Lipschitz spacetimes, we require results from causal theory when the metric is only C 0,1 . Treatments of causal theory for metrics with regularity less than C 2 can be found in [2,8,13].…”

Section: A Lipschitz Metricsmentioning

confidence: 99%

“…Our definitions of timelike and causal curves will follow the conventions in [8]. From that paper, we have the following results.…”

Section: A Lipschitz Metricsmentioning

confidence: 99%

“…Then q ∈ I + (p) by the push-up property. Following [8], a C 0 spacetime (M, g) is globally hyperbolic provided it is strongly causal and J + (p) ∩ J − (q) is compact for all p and q. Proposition A.5.…”

Section: B Asymptotics: a Class Of Examplesmentioning

confidence: 99%

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A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$ Spacetimes

Galloway

Graf

Ling

2020

Ann. Henri Poincaré

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It is well known that the spacetime AdS2×S 2 arises as the 'nearhorizon' geometry of the extremal Reissner-Nordstrom solution, and for that reason, it has been studied in connection with the AdS/CFT correspondence. Motivated by a conjectural viewpoint of Juan Maldacena, Galloway and Graf (Adv Theor Math Phys 23(2):403-435, 2019) studied the rigidity of asymptotically AdS2 × S 2 spacetimes satisfying the null energy condition. In this paper, we take an entirely different and more general approach to the asymptotics based on the notion of conformal infinity. This involves a natural modification of the usual notion of timelike conformal infinity for asymptotically anti-de Sitter spacetimes. As a consequence, we are able to obtain a variety of new results, including similar results to those in Galloway and Graf (2019) (but now allowing both higher dimensions and more than two ends) and a version of topological censorship.

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“…The following result is known as the push-up property which is proved in [8,Theorem 4.5]. See also [2,Lemma 1.15] Proposition A.2 [2,8]. Let (M, g) be a Lipschitz spacetime.…”

Section: B Asymptotics: a Class Of Examplesmentioning

confidence: 97%

Section: Next We Consider Examples Of the Following Typementioning

confidence: 99%

Section: A Lipschitz Metricsmentioning

confidence: 99%

“…Our definitions of timelike and causal curves will follow the conventions in [8]. From that paper, we have the following results.…”

Section: A Lipschitz Metricsmentioning

confidence: 99%

Section: B Asymptotics: a Class Of Examplesmentioning

confidence: 99%

See 3 more Smart Citations

A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$ Spacetimes

Galloway

Graf

Ling

2020

Ann. Henri Poincaré

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On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Geshnizjani,

Ling,

Quintin

2023

J. High Energ. Phys.

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Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended (potentially into another phase of the universe) is generally unknown. Both questions have important physical implications. In this paper, we take a closer look at the geometrical structure of inflationary spacetimes and investigate these very questions. We first classify which past inflationary histories have a scalar curvature singularity and which might be extendible and/or non-singular in homogeneous and isotropic cosmology with flat spatial sections. Then, we derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Finally, we show that beyond homogeneity and isotropy, special continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in situations with very special initial conditions.

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Time Functions on Lorentzian Length Spaces

Burtscher,

García-Heveling

2024

Ann. Henri Poincaré

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In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal structure of a spacetime and also to the initial value formulation of the Einstein equations. In this work we establish all fundamental classical existence results on time functions in the setting of Lorentzian (pre-)length spaces (including causally plain continuous spacetimes, closed cone fields and even more singular spaces). More precisely, we characterize the existence of time functions by K-causality, show that a modified notion of Geroch’s volume functions are time functions if and only if the space is causally continuous, and lastly, characterize global hyperbolicity by the existence of Cauchy time functions, and Cauchy sets. Our results thus inevitably show that no manifold structure is needed in order to obtain suitable time functions.

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Aspects of $$C^0$$ causal theory

Cited by 19 publications

References 21 publications

A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$ Spacetimes

A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$ Spacetimes

On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Time Functions on Lorentzian Length Spaces

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