Gravitational Microlensing Time Delays at High Optical Depth: Image
  Parities and the Temporal Properties of Fast Radio Bursts
  Due to differing gravitational potentials and path lengths, gravitational
lensing induces time delays between multiple images of a source which, for
solar mass objects, is of order $\sim10^{-5}$ seconds. If an astrophysically
compact source, such as a Fast Radio Burst (FRB), is observed through a region
with a high optical depth of such microlensing masses, this gravitational
lensing time delay can be imprinted on short timescale transient signals. In
this paper, we consider the impact of the parity of the macroimage on the
resultant microlensing time delays. It is found that this parity is directly
imprinted on the microlensing signal, with macroimages formed at minima of the
time arrival surface beginning with the most highly magnified microimages and
then progressing to the fainter microimages. At macroimages at the maxima of
the time arrival surface, this situation is reversed, with fainter images
observed first and finishing with the brightest microimages. For macroimages at
saddle-points, the signal again begins with fainter images, followed by
brighter images before again fading through the fainter microimages. The
growing populations of cosmologically distant bursty transient sources will
undoubtedly result in the discovery of strong lensed, multiply imaged FRBs,
which will be susceptible to microlensing by compact masses. With the temporal
resolution being offered my modern and future facilities, the detection of
microlensing induced time delays will reveal the parities of the gravitational
lens macroimages, providing additional constraints on macrolensing mass models
and improving the efficacy of these transient sources as a cosmological probes.
