Effect of gravitational wave on shadow of a Schwarzschild black hole

Understand

We have studied the shadows of a Schwarzschild black hole under a special polar gravitational perturbation, which is a particular solution of Einstein equations expanded up to first order.

• It is shown that the black hole shadow changes periodically with time and the change of shadow depends on the Legendre polynomial order parameter l and the frequency {\sigma} of gravitational wave.
• For the odd order of Legendre polynomial, the center of shadow oscillates along the direction which is vertical to equatorial plane.
• For even l, the center of shadow does not move, but the shadow alternately stretches and squeezes with time along the vertical direction.