  The time dependent conformally-flat spherical Rindler spacetime is
investigated. The geometry has an apparent horizon that coincides with the
causal horizon. The scalar acceleration of a static observer is constant and
equals to the acceleration $g$ from the static expression of the Rindler-like
metric. The timelike radial geodesics are computed and proves to be hyperbolae
when a specific choice of the constants of integration is operated.
