Regular Black Hole Cores via Gravitational Evanescence of Collapsing Matter

Modified Einstein's equations implementing both an energy-dependent Newtonian and cosmological constant can be obtained via a modified action characterised by a non-minimal gravity-matter coupling. We show how different dynamics for the high energy regime - that nevertheless have in common the vanishing of the Newton constant - result in models of gravitational collapse which source the formation of non-singular geometries with different types of asymptotic core: de Sitter, Minkowski, and with "steep pressure". As we categorise their defining properties, one feature, which we prove to be actually independent of both the specific form of the non-minimal coupling and the equation of state of the collapsing fluid, stands out: the formation of a geometry with Minkowski core occurs only if the Newton constant, before finally vanishing, assumes negative values.