  The first part of this paper discusses a model for the theoretical
construction of a simple traversable wormhole with zero density that depends on
a preexisting black hole. By assuming the interconvertibilty of black holes and
wormholes proposed by S.A. Hayward, it is shown that a toy model suggested by
the first model may yield several possible transitions from the preexisting
black hole to a wormhole. A final topic is the conversion to a wormhole by
assuming a specific model for the exotic matter.
