  In Kaluza-Klein models with an arbitrary number of toroidal internal spaces,
we investigate soliton solutions which describe the gravitational field of a
massive compact object. We single out the physically interesting solution
corresponding to a point-like mass. For the general solution we obtain
equations of state in the external and internal spaces. These equations
demonstrate that the point-like mass soliton has dust-like equations of state
in all spaces. We also obtain the PPN parameters, which give the possibility to
obtain the formulas for perihelion shift, deflection of light and time delay of
radar echoes. Additionally, the gravitational experiments lead to a strong
restriction on the parameter of the model: $\tau = -(2.1\pm 2.3)\times
10^{-5}$. The point-like mass solution contradicts this restriction. The
condition $\tau=0$ satisfies the experimental limitation and defines a new
class of solutions which are indistinguishable from general relativity. We call
such solutions latent solitons. Black strings and black branes belong to this
class. Moreover, the condition of stability of the internal spaces singles out
black strings/branes from the latent solitons and leads uniquely to the black
string/brane equations of state $p_i=-\epsilon/2$, in the internal spaces and
to the number of the external dimensions $d_0=3$. The investigation of
multidimensional static spherically symmetric perfect fluid with dust-like
equation of state in the external space confirms the above results.
