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

Chen, Songbai; Wang, Jieci; Jing, Jiliang

doi:10.1140/epjc/s10052-020-7641-3

Cited by 43 publications

(34 citation statements)

References 52 publications

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“…In literature, the theory of black hole shadows is well-developed and is under investigation for decades. Some notable results of black hole shadows are already discussed in the literature, to list a few: Schwarzschild black hole surrounded by a Bach-Weyl ring [7]; Einstein-dilaton-Gauss-Bonnet black hole [8]; Konoplya-Zhidenko or more general parameterized black holes [9,10]; Einstein-Maxwell-Chern-Simon black hole [11]; Einstein-Maxwell-Dilaton-Axion black hole [12]; Kerr-Newman-Kasuya black hole [13]; Kerr-Perfect fluid dark matter black hole [14]; Kerr-de Sitter black hole [15]; Kerr-MOG black hole [16,17]; rotating regular black hole [18]; Kerr-Sen black hole [19]; charged rotating black hole in f (R) gravity [20], noncommutative black holes [21], Tomimatsu-Sato spacetime [22], black hole surrounded by dark matter halo [23][24][25], shadow images of a rotating global monopole [26], testing the rotational nature of the supermassive object M87 and possible signals for extra dimensions in the shadow of M87 [27,28] etc, and also naked singularities [29,30]. Recently, there also are some interesting works about the curvature and topology of the geometry of the black hole shadows [31,32].…”

Section: Introductionmentioning

confidence: 99%

Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory

et al. 2019

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In this paper, we study the shadow cast by two types of charged and slowly rotating black holes in Eisntein-AEther theory of gravity. This two types of black holes are corresponding to two specific combinations of the coupling constants of the aether field, i.e., c14 = 0 but c123 = 0 for the first type and c123 = 0 for the second type, respectively. For both types of black holes, in addition to the mass and charge of the black holes, we show that the presence of the aether field can also affect the size of the shadow. For the first type black hole, it is shown that the shadow size increases with the parameter c13, while for the second type black hole, the shadow size still increases with c13 but decreases with the parameter c14. With these properties of these aether parameters, we also discuss the observational constraints on these parameters by using the data of the first black hole image by the Event Horizon Telescope. In addition, we also explore the effect of the aether field on the the deflection angle of light and the time delay by using the Gauss-Bonnet theorem. It is shown that, for a specific combination c123 = 0, the deflection angle/time delay is slightly affected by the aether parameter c13 at the leading order. *

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Section: Introductionmentioning

confidence: 99%

Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory

et al. 2019

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“…ward ray-tracing technique [22][23][24][25][26][27][28][29][30][31]. We evolved light rays by solving numerically the null geodesic equations ( 9)-( 12) from the observer backward in time.…”

Section: The Spacetime Of Schwarzschild Black Hole Perturbed By Gravitational Wave and Null Geodesicsmentioning

confidence: 99%

Effect of gravitational wave on shadow of a Schwarzschild black hole

2021

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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.

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“…Now, we study the shadows of Schwarzschild black hole with halos through the backward ray-tracing technique [12][13][14][15][16][17][18][19][20][21][22][23][24] by solving numerically the null geodesic equations ( 11) and (12). We assume that the static observer is locally at (r obs , θ obs ) in zero-angular-moment-observers (ZAMOs) reference frame [8], and evolved light rays from the observer backward in time.…”

Section: The Shadows Casted By Schwarzschild Black Hole With Halosmentioning

confidence: 99%

“…The superposition of a black hole and exterior matter will reorganize the space-time structure, and bring about a huge change to black hole shadow. We researched the shadows of a Schwarzschild black hole surrounded by a Bach-Weyl ring [22], and found black hole shadow becomes a "8" type shaped silhouette, and possesses self-similar fractal structures originating from the chaotic lensing. P. V. P. Cunha et al [58] researched the shadows of a black hole surrounded by a heavy Lemos-Letelier accretion disk, and found black hole shadow becomes more prolate with the increase of the accretion disk mass.…”

Section: Introductionmentioning

confidence: 99%

The surface geometry and shadow of a Schwarzschild black hole with halo

Guo¹,

Chen²,

Jing³

2021

Preprint

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We have studied the shadows of Schwarzschild black hole with a halo containing quadrupolar and octopolar terms. We found black hole shadow is oblate when the quadrupole strength Q is greater than zero, and it is prolate when Q is less than zero. Black hole shadow shifts upward when the octopolar strength O is less than zero, and shifts downward when O is greater than zero. From the observable width W , height H, oblateness K and distortion parameter δ of black hole shadow, one can determine the quadrupole strength Q and octopolar strength O of Schwarzschild black hole with halo. Black hole shadow is always a circle for the observers with the inclination angle θ obs = 0, and becomes bigger with the increase of Q or O. Black hole shadow not only becomes more prolate but also shifts upward as the quadrupole strength Q increases for the observer inclination angle θ obs = π/4. But black hole shadow shifts upward as O increases for θ obs = π/4, which is the opposite of the case of θ obs = π/2. Our results show that the quadrupolar and octopolar terms yield a series of interesting patterns for the shadow of a Schwarzschild black hole with halo.

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

Cited by 43 publications

References 52 publications

Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory

Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory

Effect of gravitational wave on shadow of a Schwarzschild black hole

The surface geometry and shadow of a Schwarzschild black hole with halo

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