On the instability of static, spherically symmetric wormholes supported by a ghost scalar field

We study the stability of a family of static, spherically symmetric wormholes supported by a ghost scalar field. We find that these objects are unstable under perturbations, both in the linear regime using perturbation theory and in the nonlinear case which we analyze by numerical means. In particular, we show that an initial perturbation may lead to the collapse of the wormhole to a black hole. We also focus on the possibility that a test particle or a photon can travel from one of the universes to the other through the throat of the wormhole before it collapses. We obtain constraints for the initial position of the test particle or photon in the home universe and the chances it has to explore the other universe and go back to the home universe before being trapped by the black hole horizon.