Solutions
The solutions of the Einstein field equations are metrics of spacetime. These metrics describe the structure of the spacetime including the inertial motion of objects in the spacetime. As the field equations are non-linear, they cannot always be completely solved (i.e. without making approximations). For example, there is no known complete solution for a spacetime with two massive bodies in it (which is a theoretical model of a binary star system, for example). However, approximations are usually made in these cases. These are commonly referred to as post-Newtonian approximations. Even so, there are numerous cases where the field equations have been solved completely, and those are called exact solutions.
The study of exact solutions of Einstein's field equations is one of the activities of cosmology. It leads to the prediction of black holes and to different models of evolution of the universe.
Read more about this topic: Einstein Field Equations
Famous quotes containing the word solutions:
“Those great ideas which come to you in your sleep just before you awake in morning, those solutions to the world’s problems which, in the light of day, turn out to be duds of the puniest order, couldn’t they be put to some use, after all?”
—Robert Benchley (1889–1945)
“Every man is in a state of conflict, owing to his attempt to reconcile himself and his relationship with life to his conception of harmony. This conflict makes his soul a battlefield, where the forces that wish this reconciliation fight those that do not and reject the alternative solutions they offer. Works of art are attempts to fight out this conflict in the imaginative world.”
—Rebecca West (1892–1983)
“Football strategy does not originate in a scrimmage: it is useless to expect solutions in a political compaign.”
—Walter Lippmann (1889–1974)