We present a complete study of geodesic motion in Gödel's universe, using the method of the effective potential. A clear physical picture of free motion and its stability in this universe emerges. A large class of geodesics have finite intervals in which the particle moves back in time ($\frac{\mathrm{dt}}{\mathrm{ds}}<0\mathrm{}$) without violation of causality. Gödel's geometry produces the important property of confinement for a large class of geodesics. We use this property to discuss the construction of a gravitational container. This structure is highly stable, since there is no singularity in its interior, and is independent of the energy of the particles contained in it.

• Received 10 August 1982

DOI:https://doi.org/10.1103/PhysRevD.27.779