The time delay between images of strongly gravitationally lensed quasars is
an established cosmological probe. Its limitations, however, include
uncertainties in the assumed mass distribution of the lens. We re-examine the
methodology of a prior work presenting a geometric probe of cosmology
independent of the lensing potential which considers differential time delays
over images, originating from spatially-separated photometric signals within a
strongly lensed quasar. We give an analytic description of the effect of the
differential lensing on the emission line spectral flux for axisymmetric Broad
Line Region geometries, with the inclined ring or disk, spherical shell, and
double cone as examples. The proposed method is unable to recover cosmological
information as the observed time delay and inferred line-of-sight velocity do
not uniquely map to the three-dimensional position within the source.Comment: 14 pages, 6 figures, Accepted MNRA