Gödel metric

The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution, found in 1949 by Kurt Gödel, of the Einstein field equations in which the stress–energy tensor contains two terms: the first representing the matter density of a homogeneous distribution of swirling dust particles (see dust solution), and the second associated with a negative cosmological constant (see Lambdavacuum solution).

General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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This solution has many unusual properties—in particular, the existence of closed time-like curves that would allow time travel in a universe described by the solution. Its definition is somewhat artificial, since the value of the cosmological constant must be carefully chosen to correspond to the density of the dust grains, but this spacetime is an important pedagogical example.