  We consider the lagrangian of a self-interacting complex scalar field
admitting generically Q-balls solutions. This model is extended by minimal
coupling to electromagnetism and to gravity. A stationnary, axially-symmetric
ansatz for the different fields is used in order to reduce the classical
equations. The system of non-linear partial differential equations obtained
becomes a boundary value problem by supplementing a suitable set of boundary
conditions. We obtain numerical evidences that the angular excitations of
uncharged Q-balls, which exist in flat space-time, get continuously deformed by
the Maxwell and the Einstein terms. The electromagnetic and gravitating
properties of several solutions, including the spinning Q-balls, are
emphasized.
