General relativity is the theory of space-time curvature. It is expressed in the language of differential geometry, the branch of mathematics that deals with the infinitesimal separation between two neighboring space-time points. Einstein's field equations fix the local geometry of space-time, but they say nothing about its global topology, how the space-time is connected to itself. Two surfaces (or space-times, but surfaces are easier to visualize) are topologically equivalent if one may be smoothly deformed into the other, without tearing. Thus, a coffee cup and a doughnut are topologically identical, but a sphere and a doughnut are not. It was the introduction of topological considerations into general relativity that led to the concept of "wormholes."

In 1916 (just one year after the publication of Einstein's seminal work), German astrophysicist Karl Schwarzchild solved the field equations to obtain the geometry outside a spherical mass, a star for example. He calculated...