In the late l940s, Kurt Gšdel made an significant contribution to relativity theory by finding a new solution to Einstein's equation. It represents a possible universe with remarkable properties. In particular, it allows for the possibility of "time travel" in a certain interesting sense. (It admits closed timelike curves that cannot be removed by passing to a covering space.)

In the first part of the talk, I will review, informally, certain basic ideas of relativity theory and then explain what the Gšdel universe "looks like". In the second part, I will consider a particular problem about the geometry of closed timelike curves in Gšdel's model and state a partial solution. The problem has a precise mathematical formulation. (As such, it is the close analogue of a very intuitive problem about closed curves in three-dimensional Euclidean space.) It also has a natural physical interpretation. The latter comes out, roughly, this way: "If you wanted to execute time travel in the Gšdel universe, and if you wanted to expend as little rocket fuel as possible (for each pound of payload in your rocket ship), what would be your best navigational strategy?"

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