Consider a Schwarzschild spacetime. If the singularity due to the point mass is removed (e.g. with an homogeneous matter distribution), does the event horizon disappear? If yes (I assume this is the case), how can be proven that there exists no event horizon if there is no singularity? May be it is enough to show that in the metric for the interior of stars (with homogeneous mass distribution) there is no change of the timelike coordinate from t to r at any r, as in case of the vacuum Schwarzschild solution for r = 2GM (Schutz p. 290)? I was not able to find an expression for the metric of the interior of stars to check this.