  In the present paper we consider special classes of tensor-multi-scalar
theories of gravity whose target-space metric admits Killing field(s) with a
periodic flow. For such tensor-multi-scalar theories we show that if the
dynamics of the scalar fields is confined on the periodic orbits of the Killing
field(s) then there exists a new type of compact objects - the
tensor-multi-scalar solitons formed by a condensation of the gravitational
scalars. The existence of the tensor-multi-scalar solitons is proven by solving
the fully non-linear eigenvalue problem which follows from the dimensional
reduction of the field equations of tensor-multi-scalar theories of gravity.
The mass of the tensor-multi-scalar solitons can range at least from the mass
of a neutron star to the mass of dark objects in the center of the galaxies in
dependence of mass(es) of the gravitational scalars and which sector of massive
scalars is excited. These facts show that the tensor-multi-scalar solitons
could have important implications for the dark matter problem. The existence of
the tensor-multi-scalar solitons points towards the possibility that the dark
matter, or part of it, is made of condensed gravitational scalars.
