We discuss the possibility that colliding dark matter particles in the form of neutralinos may be gravitationally boosted near the supermassive black hole at the Galactic center so that they can have enough collision energy to annihilate into a stau pair. Since in some phenomenologically favored supersymmetric models the mass splitting between the neutralino and the lightest stau, one of the two scalar superpartners of the tau lepton, is a few GeV, this channel may be allowed. In addition, staus can decay only into a tau lepton and another neutralino. We calculate the gamma ray spectrum and flux generated by the tau pair discussing the observability of the obtained features.