  We discuss the zero mass pointlike solutions and charged Einstein-Rosen
bridges (wormholes) that arise from the dyonic black hole solution of the
Einstein-Maxwell-dilaton theory. These massless black holes exist individually
in spacetime, different from the known massless solutions, which come in pairs
with opposite signs for their masses. In order to construct a massless object,
we choose the integration constants of the solution to have specific values.
The massless solutions present some problems: in one case the dilaton field is
complex (or the gauge field has negative kinetic energy), and in the other case
the solution has negative entropy and temperature or it is naked singularity in
the extremal limit. For the first case, the observables computed are real
quantities. This massless solution also allow the bridge construction, and we
obtain an analytical and static charged wormhole solution, which satisfies the
null energy condition.
