Distinguish Bardeen-like black holes by Gravitational lensing

Abstract

We study Bardeen-like regular black holes without Cauchy horizons via gravitational lensing. In the weak field, the deflection angle receives a positive $\ell$-dependent correction, producing a slightly larger Einstein ring. For the galaxy ESO 325-G004, the predicted ring radius is consistent with current observations. In the strong field, for Sgr A* and M87*, the asymptotic position $\theta_{\infty}$ remains identical to the Schwarzschild value; however, SDL coefficients are $\ell$-dependent, the angular separation s increases and the relative flux ratio $r_{\mathrm{mag}}$ decreases as $\ell$ increases. Time delays between relativistic images for Sgr A* and M87* also increase mildly with $\ell$. Our calculated values for these observables remain consistent with current observations. Future strong-field measurements of $\Delta T_{2,1}$, s, and $r_{\mathrm{mag}}$ may offer a viable test for regular black holes free of Cauchy horizons and may distinguish Bardeen-like from Schwarzschild black holes.