Analytical Kerr black hole lensing in the weak deflection limit

Sereno, Mauro; Luca, F. De

doi:10.1103/physrevd.74.123009

Cited by 62 publications

(122 citation statements)

References 30 publications

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“…Through lens equations (15) and (21), up to O(ǫ 3 ) order the caustic are point-like and are positioned in Our results for the critical curves shift (23) and the caustic positions (24) coincides with those found in [16] up to the post-Newtonian order.…”

Section: A Image Positionssupporting

confidence: 79%

“…Let us orient lens coordinates such that the axis θ 2 is along the projected lens angular momentum and the axis θ 1 is perpendicular to the optical axis. Following [12,13,16], one can show that up to the post-Newtonian order lensing by rotating naked singularities under consideration is equivalent to lensing by Janis-Newman-Winicour lens but shifted by…”

Section: A Image Positionsmentioning

confidence: 99%

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Gravitational lensing by rotating naked singularities

2008

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We model massive compact objects in galactic nuclei as stationary, axiallysymmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are a static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are function of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightingly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The point-like caustics drift away from the optical axis and do not depend on the scalar charge.In the strong deflection limit approximation we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis-Newman-Winicour naked singularities.

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Section: A Image Positionssupporting

confidence: 79%

Section: A Image Positionsmentioning

confidence: 99%

Gravitational lensing by rotating naked singularities

2008

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“…[16], using methods previously developed in Ref. [23]. This approximation is obtained by an expansion in the parameter…”

Section: Primary Causticmentioning

confidence: 99%

Optical caustics of Kerr spacetime: The full structure

Bozza

2008

Phys. Rev. D

133

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We present an exhaustive numerical investigation of the optical caustics in gravitational lensing by a spinning black hole for an observer at infinity. Besides the primary caustic, we examine higher order caustics, formed by photons performing one or several loops around the black hole. Our investigation covers the whole parameter space, including the black hole spin, its inclination with respect to the line of sight, the source distance, and the caustic order. By comparing our results with the available analytical approximations, we find perfect agreement in their respective domains of validity. We then prove that all caustics maintain their shape (a tube with astroidal cross-section) in the entire parameter space without suffering any transitions to different caustic shapes. For nearly extremal spin, however, higher order caustics grow so large that their cross-sections at fixed radii wind several times around the black hole. As a consequence, for each caustic order, the number of images ranges from 2 to 2(n + 1), where n is the number of loops spanned by the caustic. As for the critical curves, we note that for high values of the spin they develop a small dip on the side corresponding to prograde orbits.

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“…In these large distances the unresolved images are slightly de-magnified, radius of the Einstein ring decreases and time delay increases. Gravitational lensing of Kerr black hole is studied in weak field limits [7] where the critical curves are still circles displaced from the black hole location in the equatorial direction and the corresponding caustic is point-like. In strong deflection limits the Kerr black hole gravitational lensing is studied in ref.…”

Section: Introductionmentioning

confidence: 99%

Weak gravitational lensing of quantum perturbed lukewarm black holes and cosmological constant effect

Ghaffarnejad

Mojahedi

2017

Res. Astron. Astrophys.

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Aim of the paper is study weak gravitational lensing of quantum (perturbed) (QLBHL) and classical (CLBHL) Lukewarm black hole in presence of cosmological parameter Λ. We apply numerical method to evaluate deflection angle of bending light rays, images locations θ of sample source β = − π 4 , and corresponding magnifications µ. There is not obtained real values for Einstein rings locations θ E (β = 0) for CLBHL but we calculate them for QLBHL. As experimental test of our calculations, we choose mass M of 60 type of most massive observed galactic black holes as gravitational lens and study quantum matter fields effects on the angle of bending light rays in presence of the cosmological constant effects. We calculate locations of non-relativistic images and corresponding magnifications. Numerical diagrams show that the quantum matter effects cause to be reduce absolute values of the quantum deflection angle with respect to the classical ones. Sign of the quantum deflection angle is changed with respect to the classical values in presence of the cosmological constant. This means dominance of anti-gravity counterpart of the cosmological horizon on the bending light rays angle with respect to absorbing effects of local 60 type of observed most massive black holes. Variations of the image positions and magnifications are negligible by increasing dimensionless cosmological constant ǫ = 16ΛM 2 3. Deflection angle takes positive (negative) values for CLBHL (QLBHL) and they decrease very fast (slow) by increasing closest distance x 0 of bending light ray and/or dimensionless cosmological parameter for sample giant black holes 0.001 < ǫ < 0.01.

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Analytical Kerr black hole lensing in the weak deflection limit

Cited by 62 publications

References 30 publications

Gravitational lensing by rotating naked singularities

Gravitational lensing by rotating naked singularities

Optical caustics of Kerr spacetime: The full structure

Weak gravitational lensing of quantum perturbed lukewarm black holes and cosmological constant effect

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