Eikonal, nonlocality and regular black holes

We investigate the leading gravitational eikonal in nonlocal $D$ dimensional theories of gravity. We analyze the simplest cases of $2\rightarrow2$ massless and massive scalar scattering at tree level, studying the effects of nonlocal form factors in the gravitational sector. We give an interpretation of our results in terms of geodesic motion in effective generalized Aichelburg-Sexl geometries for the massless case, and in smeared linearized Schwarzschild metrics for the massive case in the probe limit. Combining our results for the geometries at linearized level with general requirements about the behaviour of the solutions in the core, we propose a nonlinear completion of the geometries. The resulting spacetimes describe singularity-free, asymptotically flat deformations of the Schwarzschild solution with a de Sitter core. We also analyze the main geometric and thermodynamic features of these solutions.