Effect of gravitational wave on shadow of a Schwarzschild black hole

Abstract

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 $$\sigma $$ σ 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. Moreover, the presence of the gravitational wave leads to the self-similar fractal structures appearing in the boundary of the black hole shadow. We also find that this special gravitational wave has a greater influence on the vertical direction of black hole shadow.

Testing symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87$$^*$$ and Sgr. $$\hbox {A}^*$$ results

“…We also emphasize that the plot does not reveal the shape of the shadow silhouette (for that, see Ref. [60]). Nevertheless, even if the shadow contour is distorted to any shape (like the case for the Kerr shadow which is D-shaped), the calculation for R sh can still be accomplished.…”

“…More recently, the black hole shadow was studied in Ref. [60] where chaotic behavior was shown. It is easy to see that without perturbation ( = 0), Eq.…”

“…If the backward tracing method is utilized, such as what was done in Ref. [60], an observer at r o observes chaotic shadow contours. As a final remark, it is interesting that when θ varies, we observe some nodal points in the photon trajectories, which also occurs in the photonsphere using a 3D plot.…”

“…In this paper, we will consider a black hole that is perturbed by a special type of gravitational wave as an astrophysical environment. Motivated by the paper in [60], which explored and studied how the black hole shadow behaves for timedependent metrics [61][62][63][64], we aim to provide an additional analysis by examining the behavior of the null geodesics, as well as find constraints to the gravitational parameter by the using the EHT data on M87*. Then, the behavior of the shadow radius will also be studied when it is influenced by different observer locations.…”

Quasinormal modes of self-dual black holes in loop quantum gravity

“…The QNMs of BH solutions undergoing scalar perturbations have been investigated in higher dimensional Einstein-Yang-Mills theory [27], Einstein-Born-Infeld gravity [28], dRGT massive gravity [29], and conformal Weyl gravity [15]. In addition, the QN modes of Schwarzschild BHs with Robin boundary conditions [30], the dirty BHs [31], the Kaluza-Klein BHs [32], and charged BHs with Weyl corrections [33] have been studied.…”