G\"odel-type universes in f(T) gravity

TL;DR

This paper explores causality issues in $f(T)$ gravity by analyzing G"odel-type universes, revealing conditions under which closed timelike curves can exist and how different matter sources influence causality violations.

Contribution

It demonstrates that in $f(T)$ gravity, G"odel solutions can exist with normal matter and identifies conditions for causality preservation or violation based on matter type.

Findings

Causality can be broken in $f(T)$ gravity with certain matter conditions.

Normal matter like pressureless matter can support G"odel solutions in some $f(T)$ models.

Scalar fields can prevent causality violation by making the critical radius infinite.

Abstract

The issue of causality in $f(T)$ gravity is investigated by examining the possibility of existence of the closed timelike curves in the G\"{o}del-type metric. By assuming a perfect fluid as the matter source, we find that the fluid must have an equation of state parameter greater than minus one in order to allow the G\"{o}del solutions to exist, and furthermore the critical radius $r_c$, beyond which the causality is broken down, is finite and it depends on both matter and gravity. Remarkably, for certain $f(T)$ models, the perfect fluid that allows the G\"{o}del-type solutions can even be normal matter, such as pressureless matter or radiation. However, if the matter source is a special scalar field rather than a perfect fluid, then $r_c\rightarrow\infty$ and the causality violation is thus avoided.