Causal bubbles in globally hyperbolic spacetimes

Abstract

We give an example of a spacetime with a continuous metric which is globally hyperbolic and exhibits causal bubbling. The metric moreover splits orthogonally into a timelike and a spacelike part. We discuss our example in the context of energy conditions and the recently introduced synthetic timelike curvature-dimension (TCD) condition. In particular we observe that the TCD-condition does not, by itself, prevent causal bubbling. see [11, Theorem 2.12].

Timelike Ricci bounds for low regularity spacetimes by optimal transport

“…The latter have been derived by using the localization technique from [3,Ch. 4], itself reliant on g-timelike nonbranching, which may fail below C 1,1 -regularity under synthetic timelike Ricci bounds [8].…”