Conformally Flat Space-Time with Dust Matter in f(R) Gravity

In this study, conformally flat space-times filled with dust matter is investigated in framework of f(R) gravitation theory. Exact solutions and field equations of conformally flat space-time in the presence of dust matter are obtained without using any restrictive method and approximation. It is shown that conformally flat space-times in framework of f(R) gravitation theory permit to dust matter with constant energy density. f(R) function which characterise dynamic structure of theory is obtained from solutions of field equations for constructed model. Obtained f(R) function for constructed model and viable f(R) functions, which are used to express various conditions and situations in theory, are compared. Change of the metric potential with respect to radial coordinate is examined by the help of graphic and limiting cases of the solutions are investigated. Finally, obtained results are discussed in the terms of physical and geometric aspects