Strong lensing by GUP-improved black holes

Abstract

We employ Bozza's method to calculate the deflection angle of light in the presence of the strong gravitational field generated by an improved Schwarzschild-like black hole whose metric, regular throughout the entire spacetime, was derived using the improved Generalized Uncertainty Principle (GUP). This framework incorporates effective quantum gravity corrections that resolve the physical singularity inside the black hole, quantified by a model parameter $\vert \tilde{Q}_{c}\vert$. In addition, the event horizon, the photon sphere, and the shadow radius receive modifications characterized by a second model parameter $\tilde{Q}_{b}$. Using observational properties of the supermassive black holes Messier~87$\ast$ and Sagittarius~A$\ast$ reported by the Event Horizon Telescope, we derive constraints on the parameter $\vert \tilde{Q}_{b}\vert$, namely $0 \leq \vert \tilde{Q}_{b}\vert \leq 0.3$. To the best of our knowledge, these are the first constraints reported in the literature for this improved GUP parameter. Since $\vert \tilde{Q}_{c}\vert$ does not play a significant role in the correction of the shadow radius, it was not possible to impose restrictions on its allowed values. However, it is important to consider a non-zero $\vert \tilde{Q}_{c}\vert$ in order to avoid a black hole singularity.