Eric Ling's research while affiliated with KTH Royal Institute of Technology and other places

Publications (19)

Preprint
Full-text available
In this paper we review and extend some results in the literature pertaining to spacetime topology while naturally utilizing properties of the codimension 2 null cut locus. Our results fall into two classes, depending on whether or not one assumes the presence of horizons. Included among the spacetimes we consider are those that apply to the asympt...
Preprint
Full-text available
Milne-like spacetimes are a class of $k = -1$ FLRW spacetimes which admit continuous spacetime extensions through the big bang. In a previous paper [29], it was shown that the cosmological constant appears as an initial condition for Milne-like spacetimes. In this paper, we generalize this statement to spacetimes which share similar geometrical pro...
Preprint
Full-text available
As is well known, constant mean curvature (CMC) spacelike hypersurfaces play an important role in solving the Einstein equations, both in solving the contraints and the evolution equations. In this paper we review the CMC existence result obtained by the authors in [10] and consider some new existence results motivated by a conjecture of Dilts and...
Article
It is well known that the spacetime AdS2×S2 arises as the ‘near-horizon’ 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 rigidit...
Article
Full-text available
This paper serves as an introduction to C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} causal theory. We focus on those parts of the theory which...
Article
Full-text available
We show that the big bang is a coordinate singularity for a large class of \(k = -1\) inflationary FLRW spacetimes which we have dubbed ‘Milne-like.’ By introducing a new set of coordinates, the big bang appears as a past boundary of the universe where the metric is no longer degenerate—a result which has already been investigated in the context of...
Preprint
It is well known that the spacetime $\text{AdS}_2\times S^2$ arises as the `near horizon' geometry of the extremal Reisser-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, the authors in [4] studied the rigidity of asymptotically $\text...
Preprint
This paper serves as an introduction to $C^0$ causal theory. We focus on those parts of the theory which have proven useful for establishing spacetime inextendibility results in low regularity - a question which is motivated by the strong cosmic censorship conjecture in general relativity. This paper is self-contained; prior knowledge of causal the...
Preprint
We present a physics model for a time-symmetric Milne-like universe based on the $q$-theory approach to the cosmological constant problem, supplemented by an assumed vacuum-matter energy exchange possibly due to quantum-dissipative effects. Without fine-tuning of the initial vacuum energy density, we obtain a harmless big bang singularity (with fin...
Preprint
We show that the big bang is just a coordinate singularity for $k = -1$ inflationary FLRW spacetimes. That is, it can be removed by introducing a set of coordinates in which the big bang appears as a past Cauchy horizon where the metric is no longer degenerate. In fact this past Cauchy horizon is just the future lightcone at the origin of a spaceti...
Article
Full-text available
In this note we present a result establishing the existence of a compact CMC Cauchy surface from a curvature condition related to the strong energy condition.
Article
Full-text available
It is a standard fact that trapped or marginally trapped surfaces are not visible from conformal infinity, under the usual set of conditions on matter fields and the conformal completion, provided that the cosmological constant is non-positive. In this note we show that the situation is more delicate in the presence of a positive cosmological const...
Article
Full-text available
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology...
Article
Full-text available
The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is $C^0$-inextendible. For the proof we establish that e...
Article
Full-text available
We prove that causal maximizers in $C^{0,1}$ spacetimes are either strictly timelike or strictly null. This question was posed in [16] since bubbling regions in $C^{0,\alpha}$ spacetimes ($\alpha <1$) can produce causal maximizers which contain a segment which is timelike and a segment which is null, cf. [3]. While $C^{0,1}$ spacetimes do not produ...
Article
When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes \text{O}(1,3)$, and the irreducible unitary representations are elementary particles which determine the particle's mas...
Article
The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is C0- inextendible. For the proof we make use of the re...
Article
Milne-like spacetimes are FLRW spacetimes which admit $C^0$ spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from a single point in the extension. This suggests that something physical may have happened there. Next w...
Article
The discovery over the past number of years of physically relevant black hole spacetimes that admit $C^0$ metric extensions beyond the future Cauchy horizon, while being $C^2$-inextendible, has focused attention on fundamental issues concerning the strong cosmic censorship conjecture. These issues were recently discussed in work of Jan Sbierski [16...

Citations

... On the other hand, we have witnessed in the past few years a surge in the use of non-smooth geometric methods in Mathematical Relativity. Diverse settings as cone structures [5,33], 0 metrics [18,14,19,31,38] and Lorentzian length spaces -to mention just a few-have proven useful in exploring scenarios where (metric) smoothness can not be guaranteed, as the ones linked to recent observations [15,30]. As a matter of fact, the use of non-smooth methods is not new. ...
... Milne-like spacetimes are a class of k = −1 FLRW spacetimes which admit continuous spacetime extensions through the big bang. In a previous paper [29], it was shown that the cosmological constant appears as an initial condition for Milne-like spacetimes. In this paper, we generalize this statement to spacetimes which share similar geometrical properties with Milne-like spacetimes but without the strong isotropy assumption associated with them. ...
... Setting the mean extrinsic curvature (τ := tr g k) of the hypersurface Σ as a constant over Σ allows it to play the role of time. However, one is obligated to address the issue related to the existence of a CMC hypersurface in the spacetimeM [55,56,57,58]. Luckily, our background solution (1) possesses constant mean extrinsic curvature slices, which is evident through explicit calculations. ...
... The existence of a (future) trapped surface -a compact codimension 2 spacelike submanifold with negative inward and outward (future) null expansions -has profound implication for the global structure of spacetime: most notably, under quite general causal assumptions and fairly weak energy conditions, it guarantees the existence of a non-empty black hole region [11,12] and, by Penrose's Singularity/Incompleteness Theorem, it also implies future causal geodesic incompleteness. ...
... Recently, Galloway, Ling and Sbierski [6] have proved the following result Theorem 1.1. A smooth (at least C 2 ) Lorentzian spacetime that is timelike geodesically complete and globally hyperbolic is C 0 -inextendible. ...
... For low regularity causal theory, generalizations, and various results, see [7,13,20,27,28,31,34]. For low regularity spacetime inextendibility results, see [8,14,16,19,[36][37][38]. For the singularity theorems in low regularity, see [17,18,24,25]. ...
... This was first proved in [10]. Their cosmological properties were explored in [16]. This paper aims to explore their quantum properties. ...
... The latter fact was also reflected in the formulation of the main theorem, which assumed an extrinsic condition on the three surface and the topological condition was that is not a handlebody 1 . A related recent result for the globally hyperbolic case in a setting compatible with a positive cosmological constant was given in [17], providing a precise connection between the topology of a future expanding compact Cauchy surface and the existence of past singularities. ...
... This point of view nicely complements recent work by Jan Sbierski [Sbi18] who showed that the Schwarzschild solution cannot be extended as a continuous 18 spacetime. In a similar vein it has been established in [GLS18] that timelike geodesic completeness remains an obstruction to extendability also in the class of C 0 -spacetimes. ...
... Sämann [25] stable causality and global hyperbolicity and their characterizations. Galloway and Ling [9,17] proved the C 0 inextendibility of AdS spacetime and showed extendibility through the Big Bang of Milne-like hyperbolic FLRW spacetimes. Chruściel and Klinger obtained a C 0 -inextendibility criterion for expanding singularities [5]. ...