Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes

Abstract

We study the deflection and gravitational lensing (GL) of both timelike and null signals in the equatorial plane of arbitrary stationary and axisymmetric spacetimes in the strong deflection limit. Our approach employs a perturbative method to show that both the deflection angle and the total travel time take quasi-series forms $\sum _{n=0}\left[C_n\ln (1-b_c/b)+D_n\right](1-b_c/b{)}^n$, with the coefficients $C_n$ and $D_n$ incorporating the signal velocity and finite distance effect of the source and detector. This new deflection angle allows us to establish an accurate GL equation from which the apparent angles of the relativistic images and their time delays are found. These results are applied to the Kerr and the rotating Kalb-Ramond (KR) spacetimes to investigate the effect of the spacetime spin in both spacetimes, and the effective charge parameter and a transition parameter in the rotating KR spacetime on various observables. Moreover, using our approach, the effect of the signal velocity and the source angular position on these variables is also studied.

arXiv comment15 pages, 10 figures; updated to publish version

References in corpus (44)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• A direct empirical proof of the existence of dark matter
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Multi-messenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A
• Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert
• Schwarzschild black hole lensing
• Gravitational lensing in the strong field limit
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Cosmic Shear
• Shadows and strong gravitational lensing: a brief review
• Evidence for neutrino emission from the nearby active galaxy NGC 1068
• Dark Energy vs. Modified Gravity
• Dark Energy Survey Year 1 Results: Constraints on Extended Cosmological Models from Galaxy Clustering and Weak Lensing
• Gravitational Lensing by Black Holes
• Combining Strong and Weak Gravitational Lensing in Abell 1689
• Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem
• The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits
• Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I: Static, Spherically Symmetric Case
• Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes
• Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit
• Strong deflection limit analysis and gravitational lensing of an Ellis wormhole
• Gravitomagnetic bending angle of light with finite-distance corrections in stationary axisymmetric spacetimes
• Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit
• CLASH: Precise New Constraints on the Mass Profile of Abell 2261
• Time Delay in Black Hole Gravitational Lensing as a Distance Estimator
• Parametric Strong Gravitational Lensing Analysis of Abell 1689
• Strong gravitational lensing and shadow constraint from M87* of slowly rotating Kerr-like black hole
• Gravitational Lensing by Rotating Naked Singularities
• Measuring the power spectrum of dark matter substructure using strong gravitational lensing
• Shadows of parametrized axially symmetric black holes allowing for separation of variables
• Gravitational lensing of massive particles in Reissner-Nordström spacetime
• Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime
• Strong field limit analysis of gravitational lensing in Kerr-Taub-NUT spacetime
• Strong gravitational lensing by Kerr and Kerr-Newman black holes
• The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach
• Strong field gravitational lensing by hairy Kerr black holes
• Strong gravitational lensing by a rotating non-Kerr compact object
• Strong gravitational lensing for the photons coupled to Weyl tensor in a Kerr black hole spacetime
• Kerr-Newman-Jacobi geometry and the deflection of charged massive particles
• Perturbative deflection angle for signal with finite distance and general velocities
• Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow
• Strong gravitational lensing by a Konoplya-Zhidenko rotating non-Kerr compact object
• Effect of electric interaction on the deflection and gravitational lensing in the strong field limit

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