Chronology protection in $f(T)$ gravity: the case of Gott's pair of moving cosmic strings

TL;DR

This paper demonstrates that in $f(T)$ gravity, the requirement for a smooth tetrad field prevents the formation of closed timelike curves in Gott's cosmic string scenario, effectively protecting chronology without quantum considerations.

Contribution

It shows that the global tetrad smoothness condition in $f(T)$ gravity restricts boosts at the junction, preventing Gott's time machine construction.

Findings

Tetrad smoothness restricts boosts to null on junction surface.

Gott's time machine construction is invalidated in $f(T)$ gravity.

Chronology protection arises from tetrad structure, not quantum effects.

Abstract

As a consequence of the spacetime structure, defined by the tetrad field instead of the metric tensor alone, $f(T)$ gravity seems to harbor its own chronology protection agency. When Gott's pair of moving cosmic strings is considered, it is shown that the requirement of having a global parallelization -- i.e. a global smooth field of tetrads -- drastically restrict the form of the tetrads on the junction surface between the two strings. The junction conditions on the tetrad field are satisfied only if the corresponding boosts needed to put the strings in motion are null on the matching surface. This seems to throw overboard Gott's construction from the outset without the need of analyzing the divergence of the expectation value of the energy momentum tensor on the Cauchy horizon, evading in this way bothering quarrels concerning the choice of vacuum.