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Generalized Oppenheimer-Snyder Gravitational Collapse into Regular Black holes

We shall study the formation of a particular class of regular black holes from the gravitational collapse of a massive star. The inside geometry is described by spatially flat Friedmann-Robertson-Walker 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 black holes. 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 black holes 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 black holes, 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 black holes jointed smoothly to the flat Friedmann-Robertson-Walker interior metric of a polytropic star with an arbitrary index.