Related papers: Causal completions as Lorentzian pre-length spaces
In this work we study the structure of the future causal completion $\hat{M}$ of a globally hyperbolic GRW spacetime $\mathbb{R}\times_\alpha M$ using the novel notion of Lorentzian pre-length spaces. As our main result, we prove that the…
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…
The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on…
In this paper a systematic study of the causal structure and global causality properties of multiwarped spacetimes is developed. This analysis is used to make a detailed description of the causal boundary of these spacetimes. Some…
In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity,…
Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved.
In this work we introduce the taxicab and uniform products for Lorentzian pre-length spaces. We further use these concepts to endow the space $D(R\times_T X)$ of causal diamonds with a Lorentzian length space structure, closely relating its…
Inspired by some Lorentzian versions of the notion of metric and length space introduced by Kunzinger and S\"amman, and more recently, by M\"uller, and Minguzzi and S\"uhr, we revisit the notion of Lorentzian metric space in order to later…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the…
We introduce conformal transformations in the synthetic setting of metric spaces and Lorentzian (pre-)length spaces. Our main focus lies on the Lorentzian case, where, motivated by the need to extend classical notions to spaces of low…
We extend Beem's three completeness notions -- finite compactness, timelike Cauchy completeness, and Condition A -- originally defined for spacetimes, to Lorentzian length spaces and study their relationships. We prove that finite…
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…
We discuss the asymptotic structure of spacetimes, presenting a new construction of ideal points at infinity and introducing useful topologies on the completed space. Our construction is based on structures introduced by Geroch, Kronheimer,…
The goal of the paper is to introduce a convergence \`a la Gromov-Hausdorff for Lorentzian spaces, building on $\epsilon$-nets consisting of causal diamonds and relying only on the time separation function. This yields a geometric notion of…
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
It is well-known that global hyperbolicity implies that the Lorentzian distance is finite and continuous. By carefully analysing the causes of discontinuity of the Lorentzian distance, we show that in most other respects the finiteness and…
In this work we establish a version of the Bartnik Splitting Conjecture in the context of Lorentzian length spaces. In precise terms, we show that under an appropriate timelike completeness condition, a globally hyperbolic Lorentzian length…
We offer a mathematically rigorous basis for the widely held suspicion that full black hole evaporation is in tension with predictability. Based on conditions expressing the global causal structure of evaporating black hole spacetimes, we…
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly…