Three-dimensional axisymmetric sources for Majumdar–Papapetrou type spacetimes
From Newtonian potential-density pairs, we construct three-dimensional axisymmetric relativistic sources for a Majumdar–Papapetrou type conformastatic spacetime. As simple examples, we build two families of relativistic thick disks from the first two Miyamoto–Nagai potential-density pairs used in Newtonian gravity to model flat galaxies, and a three-component relativistic model of galaxy (bulge, disk and dark matter halo). We study the equatorial circular motion of test particles around such structures. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. In all examples, the relativistic effects are analyzed and compared with the Newtonian approximation. The models are considered satisfying all the energy conditions.