Optimal time travel in the Gödel universe

Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (2011), we present a candidate for the minimum total integrated acceleration closed timelike curve in the Gödel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament’s conjectured value (Malament 1984), as was already implicit in the work of Manchak (Gen. Relativ. Gravit. 51–60, 2011); however, Malament’s conjecture does seem to hold for periodic closed timelike curves.