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In the past decade, significant efforts have been devoted to the study ofRelative Locality, which aims to generalize the kinematics of relativisticparticles to a nonlocal framework by introducing a nontrivial geometry formomentum space. This paper builds upon a recent proposal to extend the theoryto curved spacetimes and investigates the behavior of horizons in certainspacetimes with this nonlocality framework. Specifically, we examine whethernonlocality effects weaken or destroy the notion of horizon in thesespacetimes. Our analysis indicates that, in the chosen models, the nonlocalityeffects do not disrupt the notion of horizon and that it remains as robust asit is in General Relativity.

Relative Locality in curved spacetimes and event horizons