Causal structures and causal boundaries

Abstract

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.

Final version. To appear in Classical and Quantum Gravity

References in corpus (8)

• Background Independent Quantum Gravity: A Status Report
• Singularity Theorems and Their Consequences
• Vanishing Scalar Invariant Spacetimes in Higher Dimensions
• Null Cones and Einstein's Equations in Minkowski Spacetime
• A poor man's positive energy theorem
• A new topology on the space of Lorentzian metrics on a fixed manifold
• How can exact and approximate solutions of Einstein's field equations be compared?
• Comment on "The double-Kerr solution" by W.B. Bonnor and B.R. Steadman

Cited by in corpus (37)

• The 1965 Penrose singularity theorem
• Hawking's singularity theorem for $C^{1,1}$-metrics
• The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
• Embedding nonrelativistic physics inside a gravitational wave
• The Causal Boundary of spacetimes revisited
• A regularisation approach to causality theory for $C^{1,1}$-Lorentzian metrics
• The causal boundary of wave-type spacetimes
• Penrose's 1965 singularity theorem: From geodesic incompleteness to cosmic censorship
• The causal ladder and the strength of K-causality. I
• The causal boundary of product spacetimes
• Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples
• Causal boundaries and holography on wave type spacetimes
• On singularities, horizons, invariants, and the results of Antoci, Liebscher and Mihich (GRG 38, 15 (2006) and earlier)
• Isocausal spacetimes may have different causal boundaries
• The universal 'energy' operator
• Differential Geometric Aspects of Causal Structures
• Anti-de Sitter Quotients: When Are They Black Holes?
• Can Quantum Particles Cross a Horizon?
• Cohomology with causally restricted supports
• On the causal properties of warped product spacetimes
• Stress and Geometry for Isotropic Singularities
• Computability of the causal boundary by using isocausality
• The Attached Point Topology of the Abstract Boundary For Space-Time
• A geometric description of the intermediate behaviour for spatially homogeneous models
• Are Causality Violations Undesirable?
• Unwrapping Closed Timelike Curves
• On the causal characterization of singularities in spherically symmetric spacetimes
• The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary
• Relativistic Localizing Processes Bespeak an Inevitable Projective Geometry of Spacetime
• The Strongly Attached Point Topology of the Abstract Boundary For Space-Time
• In a distinguishing spacetime the horismos relation generates the causal relation
• The space of light rays: Causality and $L$-boundary
• A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary
• On the invariant causal characterization of singularities in spherically symmetric spacetimes
• Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes
• Black hole singularity is a surface not a point
• Vacuum Energy in Modern Cosmology: an analysis of quantum field theory in curved spaces and its application to cosmological spacetimes