No time machines in classical general relativity

TL;DR

This paper proves that in classical general relativity, any extendible spacetime cannot contain causality-violating closed causal curves outside the initial region, implying that classical time machines cannot be constructed by humans.

Contribution

It provides a rigorous proof that classical general relativity forbids the creation of human-made time machines through causality violations.

Findings

Maximal extensions contain no closed causal curves outside initial past

Time machines, as causality-violating regions, cannot be artificially created in classical GR

Spontaneous causality violations are not ruled out

Abstract

Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).