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.

15 pages, 10 figures; updated to publish version

References in corpus (19)

• 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
• Evidence for neutrino emission from the nearby active galaxy NGC 1068
• Combining Strong and Weak Gravitational Lensing in Abell 1689
• The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits
• Strong deflection limit analysis and gravitational lensing of an Ellis wormhole
• Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit
• 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
• Shadows of parametrized axially symmetric black holes allowing for separation of variables
• Strong gravitational lensing by Kerr and Kerr-Newman black holes
• Strong field gravitational lensing by hairy Kerr black holes
• Kerr-Newman-Jacobi geometry and the deflection of charged massive particles
• 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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• Particle Deflections around Microscopic Loop Quantum Black Holes with Rigorous Quantum Parameters
• Deflection of Massive Spin-$\frac{1}{2}$ Particles around Kerr Black Hole
• Off-equatorial deflections and gravitational lensing. II. In general stationary and axisymmetric spacetimes