Black Hole Shadow Drift and Photon Ring Frequency Drift
  The apparent angular size of the shadow of a black hole in an expanding
Universe is redshift-dependent. Since cosmological redshifts change with time -
known as the redshift drift - all redshift-dependent quantities acquire a
time-dependence, and a fortiori so do black hole shadows. We find a
mathematical description of the black hole shadow drift and show that the
amplitude of this effect is of order $10^{-16}$ per day for M87$^{\star}$.
While this effect is small, we argue that its non-detection can be used to
constrain the accretion rate around supermassive black holes, as well as a
novel probe of the equivalence principle. If general relativity is assumed, we
infer from the data obtained by the Event Horizon Telescope for M87$^{\star}$ a
maximum accretion rate of $|\dot{M}/{M}| \leq 10^5 M_{\odot}$ per year. On the
other hand, in the case of an effective gravitation coupling, we derive a
constraint of $|\dot{G}/G| \leq 10^{-3}-10^{-4}$ per year. The effect of
redshift drift on the visibility amplitude and frequency of the universal
interferometric signatures of photon rings is also discussed, which we show to
be very similar to the shadow drift. This is of particular interest for future
experiments involving spectroscopic and interferometric techniques, which could
make observations of photon rings and their frequency drifts viable.
