Physical and theoretical challenges to integrable singularities

Black hole spacetimes that exhibit integrable singularities have gained considerable interest as alternatives to both regular and singular black holes. Unlike most known regular black hole solutions, these models evade the formation of an inner horizon, thereby circumventing the well-known instability issues associated with such structures. Moreover, it has been suggested that the finite tidal forces near integrable singularities may allow for a traversable extension beyond them. In this work, we present a set of arguments—both theoretical, concerning test-field perturbations and the accumulation of matter at the singularity, and practical, related to the behavior of physical probes and extended objects—with the aim of assessing the validity of the proposed integrability condition, and the feasibility of traversing such singularities. Our analysis highlights key subtleties that challenge the viability of said extensions as alternatives to regular black holes, and underscores the need for a more rigorous investigation of their physical implications.