Distinguish Bardeen-like black holes by Gravitational lensing

TL;DR

This paper investigates gravitational lensing effects of Bardeen-like regular black holes without Cauchy horizons, showing how observable lensing features depend on the parameter $ ext{ extlangle} ext{ extlangle} ext{ extlangle} ext{ extlangle} ext{ extlangle} ext{ extlangle} extlangle} and how future measurements could distinguish these from Schwarzschild black holes.

Contribution

The study provides a detailed analysis of gravitational lensing signatures of Bardeen-like black holes, highlighting observable differences from Schwarzschild black holes that can be tested with future data.

Findings

Positive $ ext{ extlangle}$-dependent correction to deflection angle in weak field.

Predicted Einstein ring radius for ESO 325-G004 matches observations.

Time delays and flux ratios vary with $ ext{ extlangle}$, offering potential observational tests.

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.