Aspects of $C^0$ causal theory

Abstract

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 theory is not assumed.

arXiv comment40 pages, 6 figures. v2: references fixed and proof of prop 3.7 fixed. v3: added acknowledgement to Mittag-Leffler program. v4: to appear in GRG

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Cited by in corpus (11)

• A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
• The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• Time functions on Lorentzian length spaces
• Causality theory of spacetimes with continuous Lorentzian metrics revisited
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• Causal completions as Lorentzian pre-length spaces
• On the asymptotic assumptions for Milne-like spacetimes
• A conformal infinity approach to asymptotically ${\text{AdS}}_2\times S^{n-1}$ spacetimes
• A lower semicontinuous time separation function for $C^0$ spacetimes
• Causal bubbles in globally hyperbolic spacetimes