  Vortex-antivortex pairs are localized excitations and have been found to be
spontaneously created in magnetic elements. In the case that the vortex and the
antivortex have opposite polarities the pair has a nonzero topological charge,
and it behaves as a rotating vortex dipole. We find theoretically, and confirm
numerically, the form of the energy as a function of the angular momentum of
the system and the associated rotation frequencies. We discuss the process of
annihilation of the pair which changes the topological charge of the system by
unity while its energy is monotonically decreasing. Such a change in the
topological charge affects profoundly the dynamics in the magnetic system. We
finally discuss the connection of our results with Bloch Points (BP) and the
implications for BP dynamics.
