Kruskal solution
The Kruskal solution (after Martin Kruskal ) is the unambiguous, maximum analytical extension of the Schwarzschild solution of the field equations of Albert Einstein's general theory of relativity .
Maximum here means that every geodesic starting from an (arbitrary) point
- can either be expanded in both directions to infinite values of the affine geodesic parameter
- or ends in an intrinsic singularity .
If the first case holds for all geodesics, the manifold is called geodetically complete , as the Minkowski metric fulfills it trivially .
Since the Kruskal solution has intrinsic singularities, it is maximal, but not complete.
The Kruskal solution is obtained by transforming both the incoming ( retarded Eddington-Finkelstein coordinates ) and the outgoing ( advanced Eddington-Finkelstein coordinates) into straight lines . The Kruskal solution receives a topological interpretation from the Einstein-Rosen bridge - also known as the wormhole .
For an explicit representation of coordinates, see Kruskal-Szekeres coordinates .
