Efficient gravitational lens optical scalars calculation of black holes with angular momentum

Abstract

We provide new very simple and compact expressions for the efficient calculation of gravitational lens optical scalars for Kerr spacetime which are exact along any null geodesic. These new results are obtained recurring to well known results on geodesic motion that exploit obvious and hidden symmetries of Kerr spacetime and contrast with the rather long and cumbersome expressions previously reported in the literature, providing a helpful improvement for the sake of an efficient integration of the geodesic deviation equation on Kerr geometry. We also introduce a prescription for the observer frame which captures a new notion of \emph{center of the black hole} which can be used for any position of the observer, including those near the black hole. We compare the efficient calculation of weak lens optical scalars with the exact equations; finding an excellent agreement.

arXiv comment17 pages, 11 figures

References in corpus (22)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• 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
• Gravitational Lensing by Rotating Naked Singularities
• Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar
• Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses
• Analytical Kerr black hole lensing in the weak deflection limit
• Light's Bending Angle in the Equatorial Plane of a Kerr Black Hole
• Lensing by Kerr Black Holes. II: Analytical Study of Quasi-Equatorial Lensing Observables
• Magnification relations for Kerr lensing and testing Cosmic Censorship
• Can we see a rotating gravitational lens?
• Constraint on the black-hole spin of M87 from the accretion-jet model
• Lensing by Kerr Black Holes. I: General Lens Equation and Magnification Formula
• Intrinsic angular momentum in general relativity
• Gravitational lens optical scalars in terms of energy-momentum distributions
• Separability of Rotational Effects on a Gravitational Lens
• Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case
• Gravitational lens optical scalars in terms of energy-momentum distributions in the cosmological framework
• Mapping weak lensing distortions in the Kerr metric

Cited by in corpus (3)

• Strong gravitational lens image of the M87 black hole with a simple accreting matter model
• Schwarzschild Lensing From Geodesic Deviation
• Synthetic gravitational lens image of the Sagittarius A${}^{\ast }$ black hole with a thin disk model