Gödel-type universes in f(T) gravity

The issue of causality in $f(T)$ gravity is investigated by examining the possibility of existence of the closed timelike curves in the Gödel-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 Gödel 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 Gödel-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.

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