Gravitational Lensing and Image Distortion by Buchdahl Inspired Metric in ${\mathcal{R}}^2$ Gravity

Abstract

We investigate gravitational lensing by \textit{special} Buchdahl inspired metric with the Buchdahl parameter $\tilde{k}$. In strong deflection limit, we derive the deflection angle analytically for the light rays that diverge as photons approach the photon sphere. These are then used in order to compute the angular image positions modeling supermassive black holes, Sgr A* and M87* as lenses. The Einstein rings for the outermost relativistic images are also depicted here alongside observational constraints on $\tilde{k}$ by the Einstein radius and lens mass. Constraints on $\tilde{k}$ are obtained modelling black holes ( Sgr A* and M87*) and Canarias Einstein ring. In weak deflection limit, the analytic expression of deflection angle of the subject asymptotically flat metric in ${\mathcal{R}}^2$ gravity is determined using the Gauss Bonnet theorem. Considering M87* as a lens, weak deflection angle is used to study the image magnification and image distortion for primary and secondary images. It is shown that image distortion satisfies the hypothesis of Virbhadra. Moreover, it is seen that our general expression of deflection angle reduces, as a special case, to the deflection angle of Schwarzschild metric in both weak and strong deflection limits.

21 pages, 7 figures. To appear in Annals of Physics

References in corpus (18)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration
• First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime
• Distortions of images of Schwarzschild lensing
• Photon Spheres and Spherical Accretion Image of a Hairy Black Hole
• Gravitational lensing by wormholes
• Weak deflection angle of Kazakov-Solodukhin black hole in plasma medium using Gauss-Bonnet theorem and its greybody bonding
• Weak gravitational lensing and shadow of a GUP-modified Schwarzschild black hole in the presence of plasma
• Traversable Morris-Thorne-Buchdahl wormholes in quadratic gravity
• Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^2$ gravity and new anomalous properties of $R^2$ spacetimes
• Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form
• Observational tests of asymptotically flat ${\mathcal{R}}^2$ spacetimes
• Observational test of ${\mathcal{R}}^2$ spacetimes with the S2 star in the Milky Way galactic center
• A stationary axisymmetric vacuum solution for pure $R^2$ gravity

Cited by in corpus (4)

• A Study of Black Holes in $F(R)-$ModMax Gravity: Gravitational Lensing and Constraints from EHT Observations
• Strong Lensing Effect and Quasinormal Modes of Oscillations of Black Holes in $\mathbf{f}(\mathbf{R},\mathbf{T})$ Gravity Theory
• Gravitational Lensing by a Dark Compact Object in Modified Gravity and Observational Constraints from Einstein Rings
• Epicyclic oscillations and accretion disk around a special Buchdahl-inspired spacetime