Probing Loop Quantum Gravity black holes through gravitational lensing

TL;DR

This paper explores how loop quantum gravity modifies black hole lensing phenomena, predicting observable deviations in strong and weak gravitational lensing signals that could be detected by future high-resolution telescopes.

Contribution

It provides a detailed analysis of gravitational lensing by LQG black holes, including derivations of geodesics, deflection angles, and lensing observables, highlighting potential quantum gravity signatures.

Findings

LQG corrections increase deflection angles and image separations.

Deviations are within the sensitivity of next-generation VLBI telescopes.

LQG effects produce characteristic strong and weak lensing signatures.

Abstract

We investigate strong gravitational lensing by a charged loop quantum gravity (LQG) black hole obtained through the polymerisation scheme of Borges \textit{et al.} \cite{Borges:2023fog}. These effective geometries replace the Reissner--Nordstr\"om singularity with a symmetric transition surface and admit an extremal, cold remnant determined by the minimal area gap in LQG. In turn, we derive the null geodesic equations, investigate the photon effective potential, and obtain expressions for the photon-sphere radius and critical impact parameter. We compute the weak-field deflection angle and Einstein ring size, highlighting the deviations induced by the polymerisation parameter and the Barbero--Immirzi parameter. In the strong-field regime, we compute the strong deflection coefficients $(\bar{a},\bar{b})$ and evaluate the lensing observables $\theta_\infty$, $s$, and $r_{\rm mag}$. Unlike the Reissner--Nordstr\"om case, the LQG corrections enhance the deflection angle and increase the angular separation of relativistic images, with deviations growing as the geometry approaches the LQG remnant limit. We further compute the corresponding observables for Sgr~A* and M87*, finding that the quantum-gravity modifications lie within the potential sensitivity of next-generation VLBI facilities. For M87*, the angular separation $s\in(0.05712,0.19123)\,\mu\text{as}$, while it is $s\in(0.07595,0.25426)\,\mu\text{as}$ for Sgr A*. The relative flux ratio is found to lie in the range, $r_{\rm mag}\in(4.49272,5.96397)$. Our analysis demonstrates that LQG-induced corrections leave characteristic strong and weak-lensing imprints, offering a promising observational pathway to probe quantum gravity using near-future high-resolution observations.