Annihilations of weakly interacting dark matter particles provide an important signature for the possibility of indirect detection of dark matter in galaxy halos. These self-annihilations can be greatly enhanced in the vicinity of a massive black hole. We show that the massive black hole present at the centre of our galaxy accretes dark matter particles, creating a region of very high particle density. Consequently the annihilation rate is considerably increased, with a large number of e^+e^- pairs being produced either directly or by successive decays of mesons. We evaluate the synchrotron emission (and self-absorption) associated with the propagation of these particles through the galactic magnetic field, and are able to constrain the allowed values of masses and cross sections of dark matter particles.