Geometrical models for the study of astrophysical systems with spheroidal symmetry imbedded in a standard cosmology: The case of cosmic voids

Abstract: We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy distributions within a standard cosmological scenario, and therefore they allow for an improved description of a wider class of astrophysical systems from a more accurate point of view. These spacetimes can be used to describe overdensity or underdensity regions; in this work we consider the last case, that is, the description of cosmic voids. We introduce and study a model of void which is a generalization of a simpler one in spherical symmetry and we use it for the calculation of weak lensing optical scalars as a non-trivial and interesting application. In this particular example we show the rich observable features that can be found in such models.