Imperfect fluid sources for the cosmological universe

In General Relativity, Einstein field equations include second order nonlinear differential equations. The solutions of these equations are important for the understanding of the geometry of space time and the properties of matter contained. Although observed universe is homogeneous and isotropic at large scales, there are some deviations at small scales. In this thesis, the geometry of locally inhomogeneous structures at the galaxy and black hole scales are investigated and a energy-momentum tensor for an imperfect fluid is defined for the in-homogeneous structure of this type of space time. By applying this energy-momentum tensor to the Thakurta and Sultana-Dyer geometries, which are defined as cosmological black holes, the quantities such as energy density and pressure solving Einstein field equations are obtained. It was emphasized that at sufficiently large distances, these two geometries become Friedmann-Lemaître-Robertson-Walker space time.