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Observational constraints on nonlocal black holes via gravitational lensing

Rocco D’Agostino1,2,* and Vittorio De Falco3,†

  • *Contact author: rocco.dagostino@inaf.it
  • †Contact author: v.defalco@ssmeridionale.it
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Phys. Rev. D 113, 104018 – Published 11 May, 2026

DOI: https://doi.org/10.1103/7fq7-yc3b

Abstract

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 1.13σ 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.

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Phys. Rev. D 113, 104018– Published 11 May, 2026
  • Received 11 March 2026
  • Accepted 14 April 2026
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