On The Geometrical and Physical Properties of Spherically Symmetric Non-Static Space-Times: Self-Similarity

An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r=0$, and has non-vanishing expansion, acceleration and shear. Tidal forces in radial direction will not stretch an observer falling in this fluid. If the material is represented by perfect fluid, we can verify that the solution coincides with stiff matter case. In this case, the solution has zero expansion. Tidal forces in radial direction will not stretch an observer falling in this fluid and they not squeeze him in transverse directions.