Observational constraints on nonlocal black holes via gravitational lensing

In this paper, we study the gravitational lensing around the static and spherically symmetric D’Agostino-De Falco (DD) black holes, which we recently derived as perturbations of the Schwarzschild geometry within the revised Deser-Woodard theory of nonlocal gravity. We first present general analytical expressions for the deflection angle in both weak- and strong-deflection limits, explicitly relating them to the nonlocal corrections to Schwarzschild spacetime. Subsequently, we analyze lensing observables, such as the post-Newtonian effects and the black hole shadow, to constrain the DD black hole parameter space using current observational bounds. Finally, we perform a joint statistical analysis based on the Fisher information matrix, combining these findings with our previously obtained constraints from quasinormal modes. Our results indicate consistency with general relativity at the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1.13</a:mn> <a:mi>σ</a:mi> </a:math> level. This work provides a first assessment of the DD parameter space and offers new insights to probe deviations from Einstein’s gravity in view of future larger datasets.