  Stationary four-dimensional BPS solutions to gravity coupled bosonic theories
admitting a three-dimensional sigma-model representation on coset spaces are
interpreted as null geodesics of the target manifold equipped with a certain
number of harmonic maps. For asymptotically flat (or Taub-NUT) space-times such
geodesics can be directly parametrized in terms of charges saturating the
Bogomol'nyi-Gibbons-Hull bound, and classified according to the structure of
related coset matrices. We investigate in detail the ``dilaton-axion gravity''
with one vector field, and show that in the space of BPS solutions an $SO(1,2)
\times SO(2)$ classical symmetry is acting. Within the present formalism the
most general multicenter (IWP/Taub-NUT dyon) solutions are derived in a simple
way. We also discover a large new class of asymptotically flat solutions for
which the dilaton and axion charges are constrained only by the BPS bound. The
string metrics for these solutions are generically regular. Both the IWP class
and the new class contain massless solutions.
