Abstract: Thomas-Fermi approximation (TFA) and imaginary-time propagation method are used to study ground states of rotating Bose-Einstein condensates in an annular trap. Ground state density profiles of condensates experience a transition from vortex lattice phase to giant vortex phase with increase of angular frequency or with increase of width and center height of trap potential. Particularly, ground state density profiles change from a disc shape into an annulus shape with the increase of width and center height of trap potential, when angular frequency is zero. Finally, comparison between ground state density profiles, obtained by analytical method and numerical method is made. They coincide with each other.

Key words: Thomas-Fermi approximation, central hole, giant vortex