Generalized Oppenheimer–Snyder gravitational collapse into regular black holes

Abstract

We shall study the formation of a particular class of regular black holes (BHs) from the gravitational collapse of a massive star. The inside geometry is described by spatially flat Friedmann–Robertson–Walker (FRW) metric and the stellar matter is distributed uniformly without any pre-assumption about its equation of state. Our model is a generalization of Oppenheimer–Snyder collapse for regular BHs. We have obtained the density and pressure of star by applying the condition of smooth joining of metrics at the freely falling surface of star. Specifying the regular BHs to Hayward and Bardeen cases, we see that the stellar matter is described by a polytropic equation of state and moreover, for the radius smaller than a certain value, the strong energy condition becomes invalid. Then for both BHs, the interior apparent and event horizons and also the stellar surface are obtained as functions of the proper time of star. At the end, we have constructed a new two parametric family of regular BHs jointed smoothly to the flat FRW interior metric of a polytropic star with an arbitrary index.