We shall study the formation of a general regular black hole 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 evolution of 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.

In this paper, we treat 4-dimensional Einstein-Gauss-Bonnet gravity as general relativity with an effective stress-energy tensor. We will study the modified Oppenheimer-Snyder-Datt model of the gravitational collapse of a star in a 4-dimensional Einstein-Gauss-Bonnet black hole. The inside geometry of the star is described by the spatially flat Friedmann-Robertson-Walker metric and the matter is distributed uniformly without any pre-assumption about its equation of state. The exterior Einstein-Gauss-Bonnet black hole is smoothly matched to the interior geometry without the requirement of any thin shell. This gives the energy density, pressure, and the equation of state of collapsing matter. At the end, we study the time evolution of event and apparent horizons.

In this paper, we showed that gravity might have been repulsive in the first moments of the Universe! To find this, we used quantization of the anti-commuting space and derived a gravitational equation in the limit T ≫ Tp, which shows interesting behaviors. We saw that gravity is repulsive in the distances less than R = 4.37 × 10 −32 × √ M , where M is the mass of the object which gives rise to the gravitational field. Also, we calculated an acceleration of the order ≃ −3.494 × 10 52 for the first moment of the Universe (r = 0), where the temperature is T ≫ Tp. Our results can explain the inflation in the first stages of the Universe and do not have any singularity at r = 0.