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 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.
Highlights
IntroductionAnother exciting event in astrophysics and black hole physics is the first image of the supermassive black hole in the center of the giant elliptical galaxy M87, which was announced by Event Horizon Telescope (EHT) Collaboration in 2019 [11,12,13,14,15,16,17]
The detection of gravitational waves could help us to understand black hole further and to verify various gravity theories. Another exciting event in astrophysics and black hole physics is the first image of the supermassive black hole in the center of the giant elliptical galaxy M87, which was announced by Event Horizon Telescope (EHT) Collaboration in 2019 [11,12,13,14,15,16,17]
In this paper we studied the shadows of a Schwarzschild black hole perturbed by a special class of gravitational wave (3)
Summary
Another exciting event in astrophysics and black hole physics is the first image of the supermassive black hole in the center of the giant elliptical galaxy M87, which was announced by Event Horizon Telescope (EHT) Collaboration in 2019 [11,12,13,14,15,16,17]. Xanthopoulos [65] obtained a particular gravitational wave solution which meets Einstein equations expanded up to the first order in With this particular solution, one can probe the peculiar effects of gravitational wave on dynamics of test particle in black hole spacetime. Pl = Pl (cos θ ) are the usual Legendre polynomials (l > 1), σ is the frequency of gravitational wave This solution of the special class of gravitational wave (3) was obtained by Xanthopoulos [65] through solving the differential equations on metric perturbations of Reissner–Nordström black hole [68,69,70]. The special class of gravitational wave (3) is a solution of one-dimensional wave-type equations [68,69,70], and could be regarded as a perturbation caused by an uncharged particle moving in Schwarzschild black hole spacetime. It implies that the photon dynamical system is non-integrable, so the chaos could appear in the motion of photon in this spacetime (1)
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