The current study is conducted to solve some quantities, √ , ƒ and ≈ which are functions of the radial coordinate, � and time coordinate A , employing a centrally symmetric metric. In this study, a number of new cosmological solutions have also been calculated. The physical significance of the analysis is disscused in detailed. The results of this investigation illustrate that the centrally symmetric gravitational field with constant density automatically takes the shape of the steady state like universe. presented that the picture of the motion of the particles for a distant observer differs fundamentally from the one usually adopted (in Fock's metric) and does not correspond to the picture of asymptotic slowing down of the collapsing body. The energy density of the gravitational field in this case was calculated. Very recently, Samsonov and Petrov (5) made an investigation on the physical interpretation of the central symmetric gravitational-field singularities. The authors showed that the existence of singularity in the centrally symmetric gravitational field, which is interpreted as a surface with unusual physical properties, follows from equations for the action and the energy of a test particle not using Einstein equations and their solutions. In addition, a black hole is treated as a physical model of the singularity in question. To the best knowledge of the authors, no attention has been paid to solve the quantities and using a centrally symmetric metric. The centrally symmetric gravitational field with constant density automatically takes the shape of the steady state like Universe. This centrally symmetric gravitational field also satisfies the rigorous theorem known as the Birkhoff's theorem (6), which state that spherically symmetric vacuum solution of Einstein equation is necessarily the Schwarzschild solution that is, static. This theorem implies that if a spherically symmetric source like a star undergoes pulsations or changes its shape, while maintaining the spherically symmetry, it cannot radiate any disturbances in the exterior, namely, Schwarzschild exterior (7) solution can be used to describe the outside metric for several situations as spherically symmetric star is either static or it undergoes radial spherically symmetric gravitational collapse (8).