Regular Vaidya solutions of effective gravitational theories

Abstract

We initiate the study of the dynamics of spherically symmetric spacetimes beyond general relativity through exact solutions of the field equations of second-order effective gravitational theories defined solely in terms of the symmetries of the problem in four or more dimensions. We prove the existence of regular Vaidya solutions that represent the formation or change in mass of regular black holes (or black hole mimickers) due to the gravitational collapse or accretion of radiation, with the time reverse of these processes being also included as solutions. Our treatment and results are remarkable in their simplicity and the breadth of possibilities they provide for novel theoretical applications and discoveries in the context of regular gravitational collapse. For instance, we illustrate how modifications of the gravitational dynamics can cure curvature singularities through what can be interpreted as an energy transfer between matter and gravitational degrees of freedom. As another application, we show how to incorporate spacetimes frequently used in the literature, designed geometrically to represent the formation and disappearance of regular black holes, as fully dynamical solutions within this formalism.