  The Spitzer instability leads to the formation of a black hole sub-system
(BHSub) at the center of a star cluster providing energy to luminous stars
(LSs) and increasing their rate of evaporation. When the self-depletion time of
the BHSub exceeds the evaporation time of the LSs, a dark star cluster (DSC)
will appear. Using the NBODY7 code, we performed a comprehensive set of direct
\Nbody simulations over a wide range of initial conditions to study the pure
effect of the top-heaviness of the IMF on the formation of the DSC phase. In
the Galactic tidal field, top-heavy IMFs lead to the fast evaporation of LSs
and the formation of DSCs. Therefore, DSCs can be present even in the outer
region of the Milky Way (MW). To successfully transition to the DSC phase, the
MW Globular Clusters (GCs) must possess an initial BH mass fraction of
$\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.05$. For star clusters with
$\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.08$, the DSC phase will be created for
any given initial density of the cluster and Galactocentric distance. The
duration of the cluster's lifetime spent in the DSC phase shows a negative
(positive) correlation with the initial density, and Galactocentric distance of
the star cluster if $\widetilde{\mathit{M}}_\mathrm{BH}(0)\leq 0.12$
($\widetilde{\mathit{M}}_\mathrm{BH}(0)\geq 0.15$). Considering the canonical
IMF, it is unlikely for any MW GCs to enter the DSC phase. We discuss the BH
retention fraction in view of the observed properties of the GCs of the MW.
