  During the glorious success of the EHT in providing the first image of a
black hole, numerous papers have been published about the effect of different
astrophysical environments on black hole geometry. Motivated by the work on how
gravitational wave affects the shadow of a Schwarzschild black hole [Eur. Phys.
J. C 10.1140/epjc/s10052-021-09287-2], we extend it by considering a quantum
correction on the black hole through the extended uncertainty principle (EUP).
Along with this correction, we probe the gravitational wave's effect on the
null geodesics, and photonsphere, and find constraints to the gravitational
wave parameter $\epsilon$ using the black hole shadow of M87* for some given
test value for the gravitational wave frequency $\sigma$. Not only that some
nodes were found in the light trajectory, but the general behavior of paths
changes in a periodic way as the time $t$ progresses. These patterns then
confirm the chaotic formation of the shadow seen by some remote observer.
Finally, the constraint that we find for $\epsilon$ is $~10^{-10}$ orders of
magnitude for the effect of the gravitational wave to be seen at a distance of
$D = 16.8$ Mpc. As a consequence of such a value for $\epsilon$, another result
reveals that while there is are gravitational wave effect on the shadow
perceived at $D$, the deviations on the photonsphere are nearly non-existent.
Apart from Earth-based detectors for gravitational waves, the study implies the
possibility of an alternative detection method especially if a gravitational
wave source is near a lone black hole.

General Relativity and Quantum Cosmology