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. Each di-dimensional torus has its own scale factor Ci, i = 1, ..., N, which is characterized by a parameter Yi. We single out the physically interesting solution corresponding to a pointlike 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 parameterized post-Newtonian 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 parameters of the model: T = ƩNi=1 diYi = −(2, 1±2, 3)×10−5. The point-like mass solution with Y1 = . . . = YN = (1+ƩNi=1 di)−1 contradicts this restriction. The condition T = 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 with Yi = 0 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 pi = −ε/2, i = 1, . . . ,N, in the internal spaces and to the number of the external dimensions d0 = 3. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external
space confirms the above results.
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