Causality violation and the weak energy condition

In a recent publication, a time-machine solution of a new type has been described which has several advantages with respect to the previously known solutions. In this paper we show explicitly that the above time-machine solution indeed satisfies the weak energy condition, up until (and beyond) the time slice $t=\frac{1}{a}$, on which the causality violation appears. We also demonstrate that the solution can be matched to an asymptotically flat universe without violating the weak energy condition.