Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

Abstract

A perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $(1-b_c/b)$ where $b$ is the impact parameter and $b_c$ is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter $l$ and the asymptotic velocity $v$ of the signal. The BH shadow size were found to decrease slightly as $l$ increase to its critical value, and increase as $v$ decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of $l$ and decrease of $v$ will increase their values.

13 pages, 5 figures;

References in corpus (40)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• Formation and evaporation of non-singular black holes
• Gravitational lensing in the strong field limit
• Foundations of Black Hole Accretion Disk Theory
• Photon Regions and Shadows of Kerr-Newman-NUT Black Holes with a Cosmological Constant
• Gravitational Lensing by Black Holes
• Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum
• Multiple Images of a Highly Magnified Supernova Formed by an Early-Type Cluster Galaxy Lens
• On the exact gravitational lens equation in spherically symmetric and static spacetimes
• iPTF16geu: A multiply imaged, gravitationally lensed type Ia supernova
• Gravitational Lensing by Wormholes
• Can we distinguish between black holes and wormholes by their Einstein-ring systems?
• Gravitational lensing by a charged black hole of string theory
• Strong gravitational lensing by braneworld black holes
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• General-Relativistic Simulations of Three-Dimensional Core-Collapse Supernovae
• Strong field gravitational lensing in the deformed Hǒrava-Lifshitz black hole
• Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit
• A code to compute the emission of thin accretion disks in non-Kerr space-times and test the nature of black hole candidates
• Strong deflection limit of black hole gravitational lensing with arbitrary source distances
• Gravitational lensing by Einstein-Born-Infeld black holes
• Braneworld black holes in cosmology and astrophysics
• Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity
• Strong field limit analysis of gravitational retro-lensing
• Gravitational lensing by a regular black hole
• Analytical approach to strong gravitational lensing from ultracompact objects
• Gravitational lensing of massive particles in Reissner-Nordström spacetime
• Can strong gravitational lensing distinguish naked singularities from black holes?
• Retrolensing by a charged black hole
• A Note on Geodesics in Hayward Metric
• Black hole binaries: ergoregions, photon surfaces, wave scattering, and quasinormal modes
• The perturbative approach for the weak deflection angle
• Perturbative deflection angle for signal with finite distance and general velocities
• Constraining the spacetime spin using time delay in stationary axisymmetric spacetimes
• Perturbative deflection angles of timelike rays
• Universal time delay in static spherically symmetric spacetimes for null and timelike signals

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• Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes
• Time delay in the strong field limit for null and timelike signals and its simple interpretation
• Off-equatorial deflections and gravitational lensing. II. In general stationary and axisymmetric spacetimes
• Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes
• Strong field gravitational lensing of particles by a black-bounce-Schwarzschild black hole
• Angular Location of the $n^{th}$ Einstein Ring at large $n$