Some remarks on non-singular spherically symmetric space-times

A short review on spherically symmetric static regular black holes and spherically symmetric non singular cosmological space-time is presented. Several models of regular black holes, including new ones, are considered. First, a large class of regular black holes having an inner de Sitter core with the related issue of Cauchy horizon is investigated. Then, black bounce space-times, where the Cauchy horizon and therefore the related instabilities are absent, are discussed as valid alternatives of regular black holes with inner de Sitter core. Friedman-Lemaitre-Robertson-Walker space-times admitting regular bounce solutions are also discussed. In the general analysis concerning the presence or absence of singularities in the equations of motion, the role of a theorem due to Osgood is stressed.