Actually, Schwarzschild wormholes have the following properties: 1) They require no exotic matter. 2) They cannot be traversed (unless you can magically travel faster than light) 3) Are dynamic: they briefly open, then close (too fast to permit traversal) 4) Are also known as Einstein-Rosen bridges 5) Are also known as the maximally extended Schwarzschild solution to the Einstein equations 6) Possess event horizons 7) Do not allow a traveler who enters the event horizon to avoid eventual spaghettification The class of spherically symmetrical wormholes that are traversal are the so-called Morris-Thorne wormholes. These: 1) Do require exotic matter 2) Can be traversed (in principle) 3) Are static 4) Are incorrectly called Einstein-Rosen bridges 5) Are essentially symmetrical pieces of the Schwarzschild solution "glue" together at the wormhole throat 6) Do not possess event horizons 7) Do allow a travelers who enters to avoid spaghettification (if wormhole's throat radius is large enough) Source: The Physics of Stargates, Parallel Universes, Time Travel, and the Enigma of Wormhole Physics by Enrico Rodrigo. It think Rodrigo got his Ph.D. under the guy who brought the terms "wormhole" and "black hole" into physics, John Archibald Wheeler. I also believe that Wheeler is the guy that Kip Thorne did his Ph.D. under decades earlier.
