Non-static axisymmetric structures embedded in an asymptotically $$\Lambda $$CDM universe

Abstract We construct non-static adiabatic axisymmetric structures embedded in an asymptotically $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM universe from given solutions of the Poisson’s equation of Newtonian gravity, using a particular form of the metric in isotropic coordinates. The approach is used in building of a razor-thin disk source made of perfect fluid for the McVittie metric, a system composite by a Plummer-type perfect fluid razor-thin disk surrounded by an halo also of perfect fluid, and a model of Miyamoto–Nagai-type anisotropic fluid thick disks, embedded in an asymptotic $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM universe. In the especial case of spherical symmetry, we also present a family of models of expanding anisotropic thick spherical shells. Moreover, the geodesic motion of test particles in stable circular orbits around of the structures, the fulfilment of the energy conditions and principal stresses (pressure) are analyzed.