  Mathematical modeling of gravitating configurations of physical fields is one
of the priority directions of the modern theory of gravity. Most of the exact
solutions constructed within the framework of the general relativity are static
or stationary configurations. This is due to the objective complexity of
solving the Einstein equations under the assumption of nonstationarity. We
present an approach to constructing nonstationary configurations of a
spherically symmetric nonlinear real scalar field and the electromagnetic
field, which areassumed both to be minimally coupled to gravity. It is based on
the isolation of one invariant equation written in terms of the characteristic
function and scalar field potential. Using the proposed method, an exact
nonstationary solution with a nontrivial topology of space-time will be
constructed.
