Gravitational Lensing of Acoustic Charged Black Holes

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We study the gravitational lensing of acoustic charged black holes in strong and weak field limit approximations. For this purpose, we first numerically obtain the deflection limit coefficients and deflection angle in the strong field limit. We observe that the strong deflection angle α D increases with increasing magnitude of the charged parameter Q and that the strong deflection angle α D of an acoustic charged black hole with tuning parameter ξ = 4 is greater than that of a standard Reissner–Nordström black hole (ξ = 0). We also study the astrophysical consequences via strong gravitational lensing by taking the example of various supermassive black holes in the center of several galaxies and observe that the acoustic charged black hole could be quantitatively distinguished from standard Reissner–Nordström (ξ = 0) and standard Schwarzschild (ξ = 0, Q = 0) black holes. Furthermore, by using the Gauss–Bonnet theorem, we derive the weak deflection angle in the background of an acoustic charged black hole in the curved spacetime. We find that, for fixed values of the charged parameter Q and the tuning parameter (ξ = 0 or 4), the weak deflection angle σ D decreases with the impact parameter b. We also observe that the weak deflection angle σ D decreases with increasing magnitude of the charged parameter Q for a fixed value of the tuning parameter (ξ = 0 or 4). Our results suggest that the observational test for an acoustic charged black hole is indeed feasible, and it is generalized to the cases of acoustic Schwarzschild (Q = 0), standard Reissner–Nordström (ξ = 0), and standard Schwarzschild (ξ = 0, Q = 0) black holes.