  We present explicit solutions of the time-symmetric initial value
constraints, expressed in terms of freely specfiable harmonic functions for
examples of supergravity theories, which emerge as effective theories of
compactified string theory. These results are a prequisite for the study of the
time-evolution of topologically non-trivial initial data for supergravity
theories, thus generalising the "Geometrodynamics" program of Einstein-Maxwell
theory to that of supergravity theories. Specifically, we focus on examples of
multiple electric Maxwell and scalar fields, and analyse the initial data
problem for the general Einstein-Maxwell-Dilaton theory both with one and two
Maxwell fields, and the STU model. The solutions are given in terms of up to
eight arbitrary harmonic functions in the STU model. As a by-product, in order
compare our results with known static solutions, the metric in isotropic
coordinates and all the sources of the non-extremal black holes are expressed
entirely in terms of harmonic functions. We also comment on generalizations to
time-nonsymmetric initial data and their relation to cosmological solutions of
gauged so-called fake supergravities with positive cosmological constant.
