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

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Mingzhi Wang ◽  
Songbai Chen ◽  
Jieci Wang ◽  
Jiliang Jing
Keyword(s):  
Dynamical System ◽  
Black Hole ◽  
Ray Tracing ◽  
Invariant Manifolds ◽  
Schwarzschild Black Hole ◽  
Fractal Structures ◽  
Lyapunov Orbits ◽  
Self Similar ◽  
Photon Motion ◽  
Tracing Method

Abstract We have studied the shadows of a Schwarzschild black hole surrounded by a Bach–Weyl ring through the backward ray-tracing method. The presence of Bach–Weyl ring leads to that the photon dynamical system is non-integrable and then chaos would appear in the photon motion, which affects sharply the black hole shadow. The size and shape the black hole shadow depend on the black hole parameter, the Bach–Weyl ring mass and the Weyl radius between black hole and ring. Some self-similar fractal structures also appear in the black hole shadow, which originates from the chaotic lensing. We also study the change of the image of Bach–Weyl ring with the ring mass and the Weyl radius. Finally, we analyze the invariant manifolds of Lyapunov orbits near the fixed points and discuss further the formation of the shadow of a Schwarzschild black hole with Bach–Weyl ring.

scholarly journals Effect of gravitational wave on shadow of a Schwarzschild black hole

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Mingzhi Wang ◽  
Songbai Chen ◽  
Jiliang Jing
Keyword(s):  
Black Hole ◽  
Gravitational Wave ◽  
Legendre Polynomial ◽  
Vertical Direction ◽  
Einstein Equations ◽  
Schwarzschild Black Hole ◽  
Fractal Structures ◽  
Odd Order ◽  
Particular Solution ◽  
Self Similar

AbstractWe 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.

Shadow of a disformal Kerr black hole in quadratic degenerate higher-order scalar–tensor theories

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Fen Long ◽  
Songbai Chen ◽  
Mingzhi Wang ◽  
Jiliang Jing
Keyword(s):  
Black Hole ◽  
Deformation Parameter ◽  
Kerr Black Hole ◽  
Arbitrary Spin ◽  
Higher Order ◽  
Fractal Structures ◽  
Extreme Black Hole ◽  
Spin Parameter ◽  
Result Show ◽  
Self Similar

AbstractWe have studied the shadow of a disformal Kerr black hole with an extra deformation parameter, which belongs to non-stealth rotating solutions in quadratic degenerate higher-order scalar–tensor (DHOST) theory. Our result show that the size of the shadow increases with the deformation parameter for the black hole with arbitrary spin parameter. However, the effect of the deformation parameter on the shadow shape depends heavily on the spin parameter of black hole and the sign of the deformation parameter. The change of the shadow shape becomes more distinct for the black hole with the more quickly rotation and the more negative deformation parameter. Especially, for the near-extreme black hole with negative deformation parameter, there exist a “pedicel”-like structure appeared in the shadow, which increases with the absolute value of deformation parameter. The eyebrow-like shadow and the self-similar fractal structures also appear in the shadow for the disformal Kerr black hole in DHOST theory. These features in the black hole shadow originating from the scalar field could help us to understand the non-stealth disformal Kerr black hole and quadratic DHOST theory.

scholarly journals On the photon motion near a five-dimensional Schwarzschild black hole

2021 ◽  
Author(s):  
Husin Alatas ◽  
Siti Ainun Nuraeni ◽  
Ilma Livita Saptiani ◽  
Bobby Eka Gunara
Keyword(s):  
Black Hole ◽  
Schwarzschild Black Hole ◽  
Photon Motion

Field Estimation in Tunnel and Underground by Ray Tracing Method

2000 ◽  
Vol 54 (3) ◽  
pp. 46-56
Author(s):  
K. Uchida ◽  
D. Da ◽  
C. K. Lee ◽  
T. Matsunaga ◽  
T. Imai ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Ray Tracing Method ◽  
Field Estimation ◽  
Tracing Method

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

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