Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and, in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several routes to induce vortex lattice formation in a dipolar condensate.