ds^2 = \left(v_s(t)^2 f\big(r_s(t)\big)^2 - 1\right)\,dt^2 - 2v_s(t)f\big(r_s(t)\big)\,dx\,dt + dx^2 + dy^2 + dz^2.
With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by .