Topologically Charged Holonomy corrected Schwarzschild black hole lensing

In this paper, we theoretically investigate the deflection of light produced by a topologically charged Holonomy corrected Schwarzschild black hole. The study is carried out both in the weak field limit and in the strong field limit. We analytically deduced the expansions for light deflection in the two limits and, from them, we determined the observables in order to provide elements so that observational tools are able to identify these solutions. We model possible gravitational scenarios in order to verify the possible gravitational characteristics of the solution.

💡 Research Summary

The paper investigates gravitational lensing by a Schwarzschild black hole that incorporates two distinct modifications: a loop‑quantum‑gravity (LQG) inspired holonomy correction parameter a and a global‑monopole (topological charge) parameter α. The authors first present the metric (Eqs. 1‑2) in spherical coordinates, where the usual Schwarzschild factor (1‑2M/r) is multiplied by (1‑α²) to account for the angular deficit produced by the monopole, and the radial term is altered by the factor r/(r‑a) reflecting the LQG correction. The condition a < 2M and α² ≪ 1 is imposed to keep the spacetime asymptotically flat and to avoid horizons merging.

From the Lagrangian for null geodesics they derive conserved energy E and angular momentum L, leading to an effective potential V_eff = L²/