Exact relativistic models of conformastatic charged dust thick disks

We construct relativistic models of charged dust thick disks for a particular conformastatic spacetime through a Miyamoto–Nagai transformation used in Newtonian gravity to model disk like galaxies. Two simple families of thick disk models and a family of thick annular disks based on the field of an extreme Reissner–Nordström black hole and a Morgan–Morgan-like metric are considered. The electrogeodesic motion of test particles around the structures are analyzed. Also the stability of the particles against radial perturbation is studied using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models built satisfy all the energy conditions.