Strong gravitational lensing by Bardeen black holes in 4D EGB gravity: constraints from supermassive black holes

• Published in: arXiv.org 2022-07
• Main Authors: Shafqat Ul Islam, Ghosh, Sushant G, Maharaj, Sunil D
• Format: Article
• Language: English
• Subjects: Angular position; Deflection; Deviation; Elliptical galaxies; Gravitational lenses; Parameters; Space telescopes; Supermassive black holes
• ISSN: 2331-8422

Observation indicates that many nearby galaxies host supermassive central black holes. Modelling Bardeen models in four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity, with additional parameters \(\tilde{\alpha}\) and charge \(q\), as central black holes in various galaxies, we investigate gravitational lensing properties in strong deflection limits. Interestingly, the spherical photon orbit radius \(x_m\), the critical impact parameter \(u_m\), the lensing coefficient \(\bar{b}\), the deflection angle \(\alpha_D(\theta)\), angular position \(\theta_{\infty}\) are decreasing with \(q\) and \(\alpha\) whereas the other lensing coefficient \(\bar{a}\) and angular separation \(s\) have opposite behaviour. Taking the supermassive black holes Sgr A* and M87* as the lens, we also compare observable signatures of 4D EGB Bardeen black holes with those of the Schwarzschild black holes. The angular position \(\theta_\infty\) for Sgr A* \(\in\) (23.1853, \; 25.56427) \(\mu\)as, whereas for M87* it is \(\in\) ( 17.941,\; 19.7819) \(\mu\)as. Further, the angular separation \(s\), which is an increasing function of \(\tilde{\alpha}\) and \(q\) for Sgr A* and M87* differs significantly, respectively, in (0.031997,0.14895) \(\mu\)as and (0.0247, 0.1152) \(\mu\)as. The deviations of the lensing observables \(\Delta \theta_{\infty}\) and \(\Delta s\) for 4D EGB Bardeen black hole (\(\tilde{\alpha}=0.9,~q=0.09\)) from the Schwarzschild black hole, respectively, can reach up to \(2.3789~\mu\)as and \(0.11695~\mu\)as for Sgr A* , \(1.84084~\mu\)as and \(0.0905~\mu\)as for M87*. On the other hand, the relative magnification \(\in\) (4.65751,\; 6.82173). Considering twenty-two massive central black holes as lens, we also estimate the time delay \(\Delta T^s_{2,1}\) between the first and second relativistic image to find that, e.g., the time delay for Sgr A* and M87*, respectively, can reach \(\sim9.86088\)~min and \(\sim16023.93\)~min.