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A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonictrap with quadratic and quartic radial confinement is studied analytically withthe Thomas-Fermi approximation and numerically with the full time-independentGross-Pitaevskii equation. The quartic trap potential allows the rotation speed$\Omega$ to exceed the radial harmonic frequency $\omega_\perp$. In the regime$\Omega \gtrsim \omega_\perp$, the condensate contains a dense vortex array(approximated as solid-body rotation for the analytical studies). At a criticalangular velocity $\Omega_h$, a central hole appears in the condensate.Numerical studies confirm the predicted value of $\Omega_h$, even forinteraction parameters that are not in the Thomas-Fermi limit. The behavior isalso investigated at larger angular velocities, where the system is expected toundergo a transition to a giant vortex (with pure irrotational flow).Comment: 14 pages, 5 figure

Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap