  The special conformal transformation (composed by inversion - translation -
inversion) is used to generate a time dependent conformally flat spacetime. In
order to be an exact solution of Einstein's equations, we need as a source a
stress tensor corresponding to an anisotropic fluid with negative regular
energy density and positive pressures. For the static approximation, the
generators of the infinitesimal transformation resemble those recently obtained
by Majhi and Padmanabhan for the coordinate transformation leading to the "near
horizon" Schwarzschild metric in Kruskal coordinates. The static approximation
corresponds to an energy momentum tensor of $\Lambda$ - form, the "cosmological
constant" $\Lambda$ being proportional to the acceleration squared.
