In 1949, Kurt Gödel found a solution of Einstein's field equations and gave it to Einstein on his birthday . This solution describes a homogeneous, anisotropic, and rotationally symmetric spacetime in which matter takes the form of a pressure-free perfect fluid with negative cosmological constant, where closed timelike world lines exist. Theoretically, traveling along such a world line allows an observer to travel into their own past. For an astounding and detailed visualization of how an observer would perceive such a travel, see [2, 3].
The manipulate graphic reproduces the famous illustration contained in the book by Hawking and Ellis , showing photons emitted by an observer on the axis of symmetry at the bottom; the photons spiral out, expand, and reconverge at the top. Light-like geodesics are shown as well as light cones that tip as you increase producing the closed timelike curves. Further interpretations can be found in .
 S. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge: Cambridge University Press, 1973 section 5.7.
 I. Németi, J. X. Madarász, H. Andréka, and A. Andai, "Visualizing Ideas about Gödel-Type Rotating Universes," in Gödel-Type Spacetimes: History and New Developments (M. Scherfner and M. Plaue, eds.). Kurt Gödel Society: Collegium Logicum X, 2010 pp. 77–127. www.math-inst.hu/pub/algebraic-logic/godunivisu-revised.pdf.