  We consider a strongly interacting Bose-Einstein condensate in a spherical
harmonic trap. The system is treated by applying a slave-boson representation
for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the
condensate wave function that describes the dilute regime (like the
conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate
the condensate density of a rotating condensate for both the vortex-free
condensate and the condensate with a single vortex and determine the critical
angular velocity for the formation of a stable vortex in a rotating trap.
