In this paper, we study anisotropic spheres built from known static spherical solutions. In particular, we are interested in the physical consequences of a "small" departure from a physically sensible configuration. The obtained solutions smoothly depend on free parameters. By setting these parameters to zero, the starting seed solution is regained. We apply our procedure in detail by taking as seed solutions the Florides metrics, and the Tolman IV solution. We show that the chosen Tolman IV solution, and also the Heint IIa and Durg IV,V perfect fluid solutions, can be used to generate a class of parametric solutions where the anisotropic factor has features recalling boson stars. This is an indication that boson stars could emerge by "perturbing" appropriately a perfect fluid solution (at least for the seed metrics considered). Finally, starting with the Tolman IV, Heint IIa and Durg IV,V solutions, we build anisotropic gravastar-like sources with the appropriate boundary conditions.
Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres
