  In the past decade, significant efforts have been devoted to the study of
Relative Locality, which aims to generalize the kinematics of relativistic
particles to a nonlocal framework by introducing a nontrivial geometry for
momentum space. This paper builds upon a recent proposal to extend the theory
to curved spacetimes and investigates the behavior of horizons in certain
spacetimes with this nonlocality framework. Specifically, we examine whether
nonlocality effects weaken or destroy the notion of horizon in these
spacetimes. Our analysis indicates that, in the chosen models, the nonlocality
effects do not disrupt the notion of horizon and that it remains as robust as
it is in General Relativity.
