Description
Recent works in the literature have addressed how (i) black holes with de Sitter core circumvent the Hawking–Penrose (1970) singularity theorem, and (ii) geometries with either a de Sitter or Minkowski core can be obtained from effective models of asymptotically safe gravitational collapse, based on the high-energy behavior of the vanishing Newton coupling. Here, we investigate how generic black holes with Minkowski core specifically bypass the hypothesis of the singularity theorem on the convergence condition for geodesics. We prove that, independently of the generating dynamics, they always violate already the null convergence condition (NCC), differently from geometries with de Sitter core which always violate only the timelike convergence condition (TCC). Upon giving concrete examples of such non-singular black holes--typically characterized by exponential mass functions which can be either analytically expandable or not, we discuss the deeper physical feature encoded in the violation of the NCC. In particular, ingoing trajectories of the congruence of radial timelike geodesics approaching the Minkowski core of a black-hole spacetime undergo an additional phase where their focusing slows down to the point of reaching a state of fully parallel flow.