On the conformally flat Rindler-like geometry

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.