Modified Einstein’s equations implementing both an energy-dependent Newtonian and cosmological constant can be obtained via a modified action characterized by a nonminimal 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 nonsingular 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 nonminimal 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.
Antonio Panassiti (Thu,) studied this question.