Causal bubbles in globally hyperbolic spacetimes

TL;DR

This paper presents a continuous metric spacetime example that is globally hyperbolic yet exhibits causal bubbling, challenging assumptions about energy conditions and synthetic curvature constraints.

Contribution

It provides the first example of a globally hyperbolic spacetime with causal bubbling under a continuous metric, analyzing its implications for energy and curvature conditions.

Findings

Causal bubbling can occur in continuous, globally hyperbolic spacetimes.

The synthetic TCD condition alone does not prevent causal bubbling.

The example respects orthogonal splitting into timelike and spacelike parts.

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.