Chaotic shadow of a non-Kerr rotating compact object with quadrupole mass moment

Abstract

We have studied numerically the shadows of a non-Kerr rotating compact object with quadrupole mass moment, which belongs to Manko-Novikov family. The non-integrable photon motion caused by quadrupole mass moment affects sharply the shadow of the compact object. As the deviation parameter related to quadrupole mass moment is negative, the shadow of compact object is prolate and there are two disconnected main shadows with eyebrows located symmetrically on both sides of the equatorial plane. As the deviation parameter is positive, the shadow becomes oblate and the main shadow is joined together in the equatorial plane. Moreover, in this positive cases, there is a disorder region in the left of shadow which increases with the quadrupole-deviation parameter.Interestingly, we also find that Einstein ring is broken as the deviation from Kerr metric is larger than a certain critical value. This critical value decreases with the rotation parameter of black hole.Especially, the observer on the direction of rotation axis will find some concentric bright rings in the black disc. Finally, supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimated the numerical values of the observables for the black hole shadow.

Shadow of a Schwarzschild black hole surrounded by a Bach–Weyl ring

“…Along this spirit, we solve numerically the null geodesic equation (9) for each pixel in the final image with the corresponding initial condition and obtain the image of shadow in observer's sky which is composed of the pixels connected to the light rays falling down into the horizon of black hole. Since the spacetime (3) is asymptotically flat, one can expand the observer basis {et , er , eθ , eφ} as a form in the coordinate basis [11][12][13][14][15][16][17][18]20,56] eμ = e ν μ ∂ ν ,…”

“…With these quantities, one can obtain the coordinates of photon's image in observer's sky [10][11][12][13][14][15][16][17][18]20,56] x = −r pφ pr…”

“…Moreover, the recent investigations have shown that the cusp silhouette of shadow appears for a Kerr black hole with Proca hair [9] and for a Konoplya-Zhidenko rotating non-Kerr black hole [10] if the spacetime parameters lie in a certain range. Interestingly, there exist self-similar fractal structures in the black hole shadow for the cases where the photon motion is non-integrable, such as, a rotating black hole with scalar hair [11][12][13][14], a Majumdar-Papapetrou binary black hole system [15,16], Bonnor black diholes with magnetic dipole moment [17], and a non-Kerr rotating compact object with quadrupole mass moment [18]. These novel structure and patterns also appear in the shadows of a two dynamic black hole system with the positive cosmological constant [19].…”

Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field

“…This means that the dynamical system of two kind of polarized photons is non-integrable and the shape of black hole shadow will change. Due to the equation (2.28) without separable variables, we must resort to "backward ray-tracing" method [43][44][45][46][47][48][49][50][51][52][53][54] to study numerically the shadow casted by such kinds of polarized lights. In this method, the light rays are assumed to evolve from the observer backward in time and the information carried by each ray would be respectively assigned to a pixel in a final image in the observer's sky.…”

Applications of Spatial Technology in Schistosomiasis Control Programme in The People's Republic of China

“…Interestingly, there exist self-similar fractal structures in the black hole shadow for the cases where the photon motion is non-integrable, such as, a rotating black hole with scalar hair [11][12][13][14], a Majumdar-Papapetrou binary black hole system [15,16], Bonnor black diholes with magnetic dipole moment [17], and a non-Kerr rotating compact object with quadrupole mass moment [18]. These novel structure and patterns also appear in the shadows of a two dynamic black hole system with the positive cosmological constant [19].…”