Lensing by Kerr black holes. I. General lens equation and magnification formula

Aazami, Amir Babak; Keeton, Charles R.; Petters, Arlie O.

doi:10.1063/1.3642614

Cited by 34 publications

(27 citation statements)

References 26 publications

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“…The numerical evaluation of these integrals and/or complicated mathematical functions places a limit on the computational efficiency of ray-tracing codes that require large numbers of trajectories per volume. Approximate schemes have been developed for both Schwarzschild [20] and Kerr geodesics [21,22], but the tradeoffs between accuracy and computational efficiency are apparent. Here, we report an approximate approach that provides a highly accurate closed-form expression that is also computationally efficient.…”

Section: Introductionmentioning

confidence: 99%

Accurate closed-form trajectories of light around a Kerr black hole using asymptotic approximants

Beachley

Mistysyn

Faber

et al. 2018

Class. Quantum Grav.

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Highly accurate closed-form expressions that describe the full trajectory of photons propagating in the equatorial plane of a Kerr black hole are obtained using asymptotic approximants. This work extends a prior study of the overall bending angle for photons (Barlow, et al. 2017, Class. Quantum Grav., 34, 135017). The expressions obtained provide accurate trajectory predictions for arbitrary spin and impact parameters, and provide significant time advantages compared with numerical evaluation of the elliptic integrals that describe photon trajectories. To construct approximants, asymptotic expansions for photon deflection are required in various limits. To this end, complete expansions are derived for the azimuthal angle as a function of radial distance from the black hole in the far-distance and closest-approach (pericenter) limits, and new coefficients are reported for the bending angle in the weak-field limit (large impact parameter).

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Section: Introductionmentioning

confidence: 99%

Accurate closed-form trajectories of light around a Kerr black hole using asymptotic approximants

Beachley

Mistysyn

Faber

et al. 2018

Class. Quantum Grav.

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show abstract

“…as anticipated. Combining (22) with (18) Plugging in the value for all parameters, we reproduce the critical impact parameter b sc , and the corresponding radius of the innermost circular motion r sc in Figs. (4) and (5), plotted as a function of a for the Kerr black hole [32], and additionally, for the the Kerr-Newman black holes.…”

Section: Bitsmentioning

confidence: 99%

Equatorial light bending around Kerr-Newman black holes

2020

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We study the deflection angle of a light ray as it traverses on the equatorial plane of a charged spinning black hole. We provide the detailed analysis on the light ray's trajectory, and derive the closed-form expression of the deflection angle due to the black hole in terms of elliptic integrals. In particular, the geodesic equation of the light ray along the radial direction can be used to define an appropriate "effective potential". The non-zero charge of the black hole shows stronger repulsive effects to prevent light rays falling into the black hole as compared with the Kerr case. As a result, the radius of the innermost circular motion of light rays with the critical impact parameter decreases as charge Q of the black hole increases for both direct and retrograde motions. Additionally, the deflection angle decreases when Q increases with the fixed impact parameter. These results will have a direct consequence on constructing the apparent shape of a rotating charged black hole.

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“…Gravitational lensing by a spinning quantum deformed black hole will be an interesting topic, however, to our best knowledge, the metric for such a rotating black hole with quantum fluctuations is still absent. Even so, we might catch a glimpse that its gravitational-lensing signatures would be very different from those presented in this work since the spin can make the caustic shifted and distorted based on previous studies in other scenarios [138][139][140][141][142][143][144][145][146][147][148][149][150][151][152][153][154]. Meanwhile, the interpretation of the apparent size and shape of M87* observed by EHT depends heavily on a bank of the general relativistic magnetohydrodynamics of plasma around the Kerr black hole [6], which adopts many untested assumptions about accretion flow and emission physics [155].…”

Section: Conclusion and Discussionmentioning

confidence: 63%

Gravitational lensing by a quantum deformed Schwarzschild black hole

Xie

2021

Eur. Phys. J. C

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We investigate the weak and strong deflection gravitational lensing by a quantum deformed Schwarzschild black hole and find their observables. These lensing observables are evaluated and the detectability of the quantum deformation is assessed, after assuming the supermassive black holes Sgr A* and M87* respectively in the Galactic Center and at the center of M87 as the lenses. We also intensively compare these findings with those of a renormalization group improved Schwarzschild black hole and an asymptotically safe black hole. We find that, among these black holes, it is most likely to test the quantum deformed Schwarzschild black hole via its weak deflection lensing observables in the foreseen future.

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Lensing by Kerr black holes. I. General lens equation and magnification formula

Cited by 34 publications

References 26 publications

Accurate closed-form trajectories of light around a Kerr black hole using asymptotic approximants

Accurate closed-form trajectories of light around a Kerr black hole using asymptotic approximants

Equatorial light bending around Kerr-Newman black holes

Gravitational lensing by a quantum deformed Schwarzschild black hole

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