Gödel metric

The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution of the Einstein field equations. This solution has many unusual properties—in particular, the existence of closed timelike curves that would allow time travel in a universe described by the solution. Its definition is somewhat artificial in that the value of the cosmological constant must be carefully chosen to match the density of the dust grains, but this spacetime is an important pedagogical example