An extendible spacetime without closed timelike curves whose every extension contains closed timelike curves

TL;DR

This paper constructs a special spacetime by removing a fractal from Minkowski space, resulting in an extendible spacetime that lacks closed timelike curves itself but inevitably contains them in any extension, addressing a longstanding question.

Contribution

It introduces a novel spacetime model that is extendible yet has the unique property of every extension containing closed timelike curves, answering Geroch's question.

Findings

Constructed a fractal-based spacetime model

Proved the spacetime is extendible without initial closed timelike curves

Showed all extensions necessarily contain closed timelike curves

Abstract

By removing a fractal from time-rolled Minkowski spacetime, we construct an extendible spacetime without closed timelike curves whose every extension contains closed timelike curves. This settles a question posed by Geroch.