  We investigate gravitational collapses of charged black holes in
string-inspired gravity models, including dilaton gravity and braneworld model,
as well as f(R) gravity and the ghost limit. If we turn on gauge coupling, the
causal structures and the responses of the Brans-Dicke field depend on the
coupling between the charged matter and the Brans-Dicke field. For Type IIA
inspired models, a Cauchy horizon exists, while there is no Cauchy horizon for
Type I or Heterotic inspired models. For Type IIA inspired models, the no-hair
theorem is satisfied asymptotically, while it is biased to the weak coupling
limit for Type I or Heterotic inspired models. Apart from string theory, we
find that in the ghost limit, a gravitational collapse can induce inflation by
itself and create one-way traversable wormholes without the need of other
special initial conditions.
