Optimal time travel in the Godel universe

TL;DR

This paper identifies a candidate for the least-accelerated closed timelike curve in the Godel universe using optimal trajectory theory, providing evidence for its minimality and comparing it to previous conjectures.

Contribution

It introduces a new candidate for the minimal acceleration closed timelike curve in the Godel universe and analyzes its optimality compared to prior conjectures.

Findings

The candidate curve has lower total acceleration than Malament's conjecture.

Evidence supports the minimality of the proposed curve.

Malament's conjecture holds for periodic closed timelike curves.

Abstract

Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we present a candidate for the minimum total integrated acceleration closed timelike curve in the Godel 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 (Manchak, 2011); however, Malament's conjecture does seem to hold for periodic closed timelike curves.