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

Abstract

We have studied the surface geometry and shadows of Schwarzschild black hole with a halo containing the quadrupolar and octopolar terms. We found the quadrupole term makes the Schwarzschild black hole prolate for the quadrupole strength $\mathcal{Q}<0$ and oblate for $\mathcal{Q}>0$, and the octopole term makes shadow stretch upward for the octopolar strength $\mathcal{O}<0$ and stretch downward for $\mathcal{O}>0$. The shadow of Schwarzschild black hole with halo stretches and squeezes along the horizontal direction for $\mathcal{Q}<0$ and $\mathcal{Q}>0$ respectively. Meanwhile, black hole shadow shifts upward for $\mathcal{O}<0$ and shifts downward for $\mathcal{O}>0$. We exhibited the light rays that form the shadow boundary to explain the emergence of the extraordinary patterns of black hole shadow with the quadrupole and octopole terms. From the observable width $W$, height $H$, oblateness $K$ and distortion parameter ${\delta }_c$ of black hole shadow, one can determine the quadrupole and octopolar strengths of Schwarzschild black hole with halo. 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.

20 pages,12 figures

References in corpus (33)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration
• First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass
• Shadow of a black hole surrounded by dark matter
• A new method for shadow calculations: application to parameterised axisymmetric black holes
• Apparent shape of super-spinning black holes
• Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity
• Shadow of a Kaluza-Klein rotating dilaton black hole
• Photon Rings around Kerr and Kerr-like Black Holes
• Chaotic lensing around boson stars and Kerr black holes with scalar hair
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole
• Shadows of Sgr A${}^{\ast }$ Black Hole Surrounded by Superfluid Dark Matter Halo
• What does a binary black hole merger look like?
• Shadows and lensing of black holes immersed in strong magnetic fields
• Black hole shadow to probe modified gravity
• Kerr Black hole shadows in Melvin magnetic field with stable photon orbits
• Black Hole Shadows and Invariant Phase Space Structures
• Chaotic Shadows of Black Holes: A Short Review
• The observer-dependent shadow of the Kerr black hole
• On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
• Black Hole Shadows Constrain Extended Gravity
• Effect of Multipole Moments in the Weak Field Limit of a Black Hole Plus Halo Potential

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