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This is a collection of notes to calculate electromagnetic spectra of geometrically thin and optically thick accretion disks around black holes. The presentation is intentionally pedagogical and most calculations are reported step by step.…

High Energy Astrophysical Phenomena · Physics 2024-08-23 Cosimo Bambi

One of the methods of study of black holes in astrophysics is based on broadening of the spectrum of radiation of ionized Iron atoms. The line K$\alpha$ associated with Iron emission at 6.4 keV is very narrow. If such an ion is revolving…

General Relativity and Quantum Cosmology · Physics 2015-09-09 Valeri P. Frolov , Andrey A. Shoom , Christos Tzounis

In the presence of a black hole, light sources connect to observers along multiple paths. As a result, observed brightness fluctuations must be correlated across different times and positions in black hole images. Photons that execute…

General Relativity and Quantum Cosmology · Physics 2023-06-21 Shahar Hadar , Michael D. Johnson , Alexandru Lupsasca , George N. Wong

The images of supermassive black holes surrounded by optically-thin, radiatively-inefficient accretion flows, like those observed with the Event Horizon Telescope, are characterized by a bright ring of emission surrounding the black-hole…

High Energy Astrophysical Phenomena · Physics 2023-02-01 Ziri Younsi , Dimitrios Psaltis , Feryal Özel

Circular photon orbit and black hole shadow are significantly important issues in physics and astronomy, and a number of breakthroughs have been witnessed in recent years. Conventionally, the stable and unstable circular photon orbits are…

General Relativity and Quantum Cosmology · Physics 2024-09-12 Chen-Kai Qiao , Ming Li

This article computes the bending angle of a hairy black hole at weak field limits. The Gauss-Bonnet theorem is applied to the Gaussian optical curvature; this gives a way to calculate the hairy black hole light bending angle using the…

General Relativity and Quantum Cosmology · Physics 2025-02-25 Riasat Ali , Xia Tiecheng , Muhammad Awais , Rimsha Babar

Photons emitted by light sources in the neighbourhood of a black hole can wind several times around it before fleeing towards the observer. For spherically symmetric black holes, two infinite sequences of images are created for any given…

General Relativity and Quantum Cosmology · Physics 2021-10-27 F. Aratore , V. Bozza

We derive closed formulas for the mass and spin parameters of a Kerr black hole in terms of a minimal quantity of observational data: the red-/blue-shifts of photons emitted by massive particles (stars) moving on geodesics around the black…

General Relativity and Quantum Cosmology · Physics 2021-02-17 Alfredo Herrera-Aguilar , Raúl Lizardo-Castro , Ulises Nucamendi

In this article we find a four-dimensional metric for a large black hole immersed in dark matter. Specifically, we look for and find a static spherically symmetric black hole solution to the Einstein equations which gives, in the Newtonian…

General Relativity and Quantum Cosmology · Physics 2021-01-12 Fateen Haddad , Nidal Haddad

The photon sphere defines the unstable circular orbit of photons in a black hole spacetime. Photons emitted by a source located inside the photon sphere can be gravitationally lensed by the black hole and have time delays when reaching the…

High Energy Astrophysical Phenomena · Physics 2025-05-28 Yuan-Xing Gao

The presence of a bright "photon ring" surrounding a dark "black hole shadow" has been discussed as an important feature of the observational appearance of emission originating near a black hole. We clarify the meaning and relevance of…

High Energy Astrophysical Phenomena · Physics 2019-07-17 Samuel E. Gralla , Daniel E. Holz , Robert M. Wald

The combined effect of a strong gravitational field and electromagnetic field in the vicinity of a generic regular black hole related to non-linear electrodynamics with Maxwellian weak-field limit on the radiation flux of a hot spot…

General Relativity and Quantum Cosmology · Physics 2021-12-10 Dmitriy Ovchinnikov , Jan Schee , Zdenek Stuchlík , Bobomurat Ahmedov

Images from the vicinity of the black hole horizon at the Galactic centre (Sgr A*) could be obtained in the near future with a Very Large Baseline Array of sub-millimetre telescopes. The recently observed short-term infrared and X-ray…

Astrophysics · Physics 2009-11-13 Avery E. Broderick , Abraham Loeb

Most of the X-ray emission from luminous accreting black holes emerges from within 20 gravitational radii. The effective emission radius is several times smaller if the black hole is rapidly spinning. General Relativistic effects can then…

High Energy Astrophysical Phenomena · Physics 2015-06-12 A. C. Fabian

From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to…

General Relativity and Quantum Cosmology · Physics 2021-07-12 Albert Sneppen

We present a fitting function to describe the statistics of flux modulations caused by interstellar scintillation. The function models a very general quantity: the cross-correlation of the flux observed from a compact radio source of finite…

Astrophysics · Physics 2009-11-13 J. Goodman , R. Narayan

Light deviation around a rotating black hole is calculated using the Kerr metric for both small and large deviation angles. For small angles the Lindstedt-Poincar\'e method is employed to get well-behaved solutions, as well as Pad\'e…

General Relativity and Quantum Cosmology · Physics 2021-12-16 Pablo Ruales , Carlos Marín

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the…

General Relativity and Quantum Cosmology · Physics 2017-06-29 Nathaniel S. Barlow , Steven J. Weinstein , Joshua A. Faber

We present raytracing computations for light emitted from the surface of a rapidly-rotating neutron star in order to construct light curves for X-ray pulsars and bursters. These calculations are for realistic models of rapidly-rotating…

Astrophysics · Physics 2011-02-11 Coire Cadeau , Sharon M. Morsink , Denis Leahy , Sheldon S. Campbell

The scalar radiation emitted by a source in geodesic circular orbit around a regular Bardeen black hole is analyzed. We use the quantum field theory in curved spacetime framework to obtain the emitted power of radiation by computing the…

General Relativity and Quantum Cosmology · Physics 2019-07-17 R. P. Bernar , L. C. B. Crispino