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One of the leading scenarios for the formation of nuclear star clusters ingalaxies is related to the orbital decay of globular clusters (GCs) and theirsubsequent merging, though alternative theories are currently debated. Theavailability of high-quality data for GCs structural and orbital parametersallow to test different nuclear star cluster formation scenarios. The Fornaxdwarf spheroidal (dSph) galaxy is the heaviest satellite of the Milky Way andit is the only known dwarf spheroidal hosting 5 GCs, whereas there are no clearsignatures for the presence of a central massive black hole. For this reason,it represents a suited place to study the orbital decay process in dwarfgalaxies. In this paper we model the future evolution of the Fornax GCssimulating them and the host galaxy by means of direct $N$-body simulations.Our simulations take in account also the gravitational field generated by theMilky Way. We found that if the Fornax galaxy is embedded in a standard ColdDark Matter Halo, the nuclear cluster formation would be significantly hamperedby the high central galactic mass density. In this context, we discuss thepossibility that infalling GCs drive the flattening of the galactic densityprofile, giving a possible alternative explanation to the so-called cusp/coreproblem. Moreover, we briefly discuss the link between GC infall process andthe absence of massive black holes in the centre of dSphs.

Lack of nuclear clusters in dwarf spheroidal galaxies: implications for massive black holes formation and the cusp/core problem