Poisson type conformastat spherically symmetric anisotropic fluid spacetimes

Abstract

We construct conformastat spherically symmetric spacetimes representing anisotropic fluid matter distributions from given solutions of the Poisson’s equation of Newtonian gravity and its corresponding circular speed profile. As simple examples, we present three families of spherically symmetric spacetimes which we apply in constructing new models of relativistic anisotropic thick spherical shells, and of relativistic galaxy models composite by a central spherical bulge, the thick disk and the dark matter halo, writing in this case the metric in cylindrical coordinates. Moreover, the geodesic motion of test particles in stable circular orbits around such structures is studied. We build anisotropic fluid sources for these spacetimes which satisfy all the energy conditions and the principal stresses are positive quantities (pressure).