Interest in regular black holes, such as the Hayward and Simpson-Visser geometries, has grown considerably in recent years as effective models for exploring possible resolutions of singularities in General Relativity. However, many of these geometries are specified at the metric level, rather than derived from a parent theory. When interpreted within General Relativity, they often require matter sectors tailored to support the prescribed regular geometry. The main objective of this work is to address this issue from the inverse perspective, following the method introduced by Suvorov. Unlike the standard approach in gravitational dynamics, where one starts from an action and subsequently solves the equations of motion, here we start from a prescribed regular geometry, from which we construct a mixed scalar-f(R) theory admitting the geometry as an exact vacuum solution. After reviewing the necessary theoretical background, we apply this procedure to the Hayward and Simpson-Visser geometries. We first perform the reconstruction in the exterior region, showing that the functional choices introduced by Suvorov with a vanishing scalar potential are too restrictive for these regular metrics, since they do not allow real scalar profiles in the domains of interest. We then introduce suitable non-zero scalar potentials, which make the reconstruction possible and lead to regular scalar configurations with the appropriate asymptotic behaviour. Once the exterior reconstruction is completed, we extend the analysis across the horizons using advanced Eddington-Finkelstein coordinates and adapting the choice of potential, while preserving the appropriate asymptotic behaviour. The results show that both regular metrics can be interpreted as exact vacuum solutions of suitable mixed scalar-f(R) theories. This approach then provides a way to interpret regular metrics originally proposed at the metric level within a specific modified-gravity theory, thereby avoiding the introduction of an external matter source designed to support them.
2026-07-15
