  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.
