Black Holes, Wormholes, and Time Machines

Abstract

One of the most intriguing features of the theory of general relativity is the possible existence of spacetimes with non-trivial topological structure. The wormhole solutions of the Einstein equations described by Wheeler [Misner and Wheeler (1957), Wheeler (1962)] are well-known examples of spaces with non-trivial topology. The simplest example of such a spacetime is the Einstein-Rosen bridge described in Chapter 2. The spacetime of an eternal black hole can be considered as the evolution of the Einstein-Rosen bridge. To the future of the moment of time symmetry the throat shrinks to zero size and the singularity arises. No causal signal can propagate through the throat from one asymptotically flat region (R₊) to the other one (R₊). This property is directly connected with the non-trivial causal structure of spacetime in the presence of a black hole