What does the Gdel solution, proposed to Einstein's equations, imply as a technical possibility?
Time travel causal future of the world line is also in its causal past, a situation which is akin to time travel. Such a solution was first proposed by Kurt Gödel, a solution known as the Gödel metric, but his (and others') solution requires the universe to have physical characteristics that it does not appear to have, such as rotation and lack of Hubble expansion. Whether general relativity forbids closed time-like curves for all realistic conditions is still being researched. Wormholes are a hypothetical warped spacetime which are permitted by the Einstein field equations of general relativity. A proposed time-travel machine using
Einstein field equations of nonzero cosmological constant, the equations are The solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution. Manifolds with a vanishing Ricci tensor, , are referred to as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds. If the energy-momentum tensor is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor is used, then the Einstein field equations are called the "Einstein–Maxwell equations" (with cosmological constant ,