Weak Deflection angle and Shadow by Tidal Charged Black Hole

TL;DR

This paper calculates the weak gravitational lensing deflection angle and shadow of tidal charged black holes using the Gauss-Bonnet theorem, including effects of plasma medium, and compares results with observational parameters from M87*.

Contribution

It introduces a novel application of the Gauss-Bonnet theorem to compute light deflection and shadow of tidal charged black holes, including plasma effects, which is a new approach in this context.

Findings

Derived the deflection angle of TCBH in weak field limits.

Analyzed the shadow radius of TCBH with and without plasma medium.

Compared the shadow characteristics with M87* observational data.

Abstract

In this article, we calculate the deflection angle of tidal charged black hole (TCBH) in weak field limits. First we obtain the Gaussian optical curvature and then apply the Gauss-Bonnet theorem on it. With the help of Gibbons-Werner method, we are able to calculate the light's deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light's deflection angle in the presence of plasma medium and also check the graphical behavior in the presence of plasma medium. Moreover, we investigate the shadow of TCBH. For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH's shadow in the plasma medium. Hence, we discuss the shadow of the TCBH using the $M87^{*}$ parameters announced by the Event Horizon Telescope.