Constraining a one-dimensional wave-type gravitational wave parameter through the shadow of M87* via Event Horizon Telescope

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.