On effective models of regular black holes inspired by higher-derivative and nonlocal gravity

In this work we study static spherically symmetric solutions of effective field equations related to local and nonlocal higher-derivative gravity models, based on their associated effective delta sources. This procedure has been applied to generate modifications of the Schwarzschild geometry in several contexts (e.g., modified gravity, string theory, noncommutative geometry, generalized uncertainty principle scenarios), but a general analysis of the possible equations of state and their influence on the solutions was still lacking. Here, we aim to fill this gap in the literature and investigate whether these metrics might be able to reproduce features of the solutions of higher-derivative gravity models. In particular, we present an equation of state such that the solution matches the Newtonian-limit one in both regimes of large and small r. A significant part of the work is dedicated to studying the curvature regularity of the solutions and the comparison with the linearized solutions. Explicit metrics are presented for effective sources originating from local and nonlocal models. The results obtained here might be regarded as possible links between the previous research on linearized higher-derivative gravity and the solutions of the nonlinear complete field equations, which remain unknown at the moment.