Effect of gravitational wave on shadow of a Schwarzschild black hole

We have studied the shadows of a Schwarzschild black hole under special polar gravitational perturbation, which is particular solution Einstein equations expanded up to first order. It shown that shadow changes periodically with time and change depends on Legendre polynomial order parameter l frequency {\sigma} wave. For odd polynomial, center oscillates along direction vertical equatorial plane. even l, does not move, but alternately stretches squeezes direction. Moreover, presence wave leads self-similar fractal structures appearing in boundary shadow. also find this has greater influence