On the causal hierarchy of Lorentzian length spaces

Abstract

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 simplicity, causal continuity, stable causality and strong causality are preserved under distance homothetic maps.

arXiv commentThe notion of weakly locally causally closed sets has been introduced. Other details brought to our attention by the referees have been addressed. See the accepted version by Classical and Quantum Gravity for the latest changes (https://doi.org/10.1088/1361-6382/abb25f)

References in corpus (20)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• Causality theory for closed cone structures with applications
• On Lorentzian causality with continuous metrics
• A Causal Order for Spacetimes with $C^0$ Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves
• Global hyperbolicity for spacetimes with continuous metrics
• Timelike completeness as an obstruction to $C^0$-extensions
• Singularity theorems for $C^1$-Lorentzian metrics
• The Penrose singularity theorem in regularity $C^{1,1}$
• K-causality coincides with stable causality
• The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
• Some Remarks on the $C^0$-(in)extendibility of Spacetimes
• A regularisation approach to causality theory for $C^{1,1}$-Lorentzian metrics
• Globally hyperbolic spacetimes can be defined without the 'causal' condition
• Structure of globally hyperbolic spacetimes with timelike boundary
• Gravity and Matter in Causal Set Theory
• Dynamics for causal sets with matter fields: A Lagrangian-based approach
• Path length distribution in two-dimensional causal sets

Cited by in corpus (17)

• Null distance and convergence of Lorentzian length spaces
• The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
• The singularity theorems of General Relativity and their low regularity extensions
• A Lorentzian analog for Hausdorff dimension and measure
• Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
• Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds
• The Null distance encodes causality
• Causality theory of spacetimes with continuous Lorentzian metrics revisited
• Gluing constructions for Lorentzian length spaces
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• Causal completions as Lorentzian pre-length spaces
• Gluing of Lorentzian length spaces and the causal ladder
• Further observations on the definition of global hyperbolicity under low regularity
• A lower semicontinuous time separation function for $C^0$ spacetimes
• A Toponogov globalisation result for Lorentzian length spaces
• The representation of spacetime through time functions