  In this letter, we consider the six-dimensional Kaluza-Klein models with
spherical compactification of the internal space. Here, we investigate the case
of bare gravitating compact objects with the dustlike equation of state $\hat
p_0=0$ in the external (our) space and an arbitrary equation of state $\hat
p_1=\Omega \hat\varepsilon$ in the internal space, where $\hat \varepsilon$ is
the energy density of the source. This gravitating mass is spherically
symmetric in the external space and uniformly smeared over the internal space.
In the weak field approximation, the conformal variations of the internal space
volume generate the admixture of the Yukawa potential to the usual Newton's
gravitational potential. For sufficiently large Yukawa masses, such admixture
is negligible and the metric coefficients of the external spacetime coincide
with the corresponding expressions of General Relativity. Then, these models
satisfy the classical gravitational tests. However, we show that gravitating
masses acquire effective relativistic pressure in the external space. Such
pressure contradicts the observations of compact astrophysical objects (e.g.,
the Sun). The equality $\Omega =-1/2$ (i.e. tension) is the only possibility to
preserve the dustlike equation of state in the external space. Therefore, in
spite of agreement with the gravitational experiments for an arbitrary value of
$\Omega$, tension ($\Omega=-1/2$) plays a crucial role for the considered
models.
