A note on the causal homotopy classes of a globally hyperbolic spacetime

TL;DR

This paper explores the existence of globally hyperbolic spacetimes with infinitely many distinct causal and timelike homotopy classes of curves connecting the same two points, highlighting complex causal structures.

Contribution

It demonstrates the existence of such spacetimes and discusses their properties, advancing understanding of causal homotopy classes in Lorentzian geometry.

Findings

Existence of spacetimes with infinitely many causal homotopy classes

Discussion of properties of these spacetimes

Implications for causal structure theory

Abstract

Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.