Motivated by quantum-mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which measures the perimeter of the space-time and has a dimension of length. It is the so called perimeter/linear action, since it is a "square root" of the area action in gravity and has a new constant of dimension one in front. The physical reason to introduce the perimeter/linear action was to suppress singular configurations "spikes" in the quantum-mechanical integral over geometries. Here we shall consider the continuous limit of the discretised perimeter action. We shall demonstrate that in the modified theory during the time evolution of a large massive star, when a star undergoes a collapse and develops an event horizon which confines the light, a smaller space-time region will be created behind the event horizon which is unreachable by test particles. These regions are located in the places where a standard theory of gravity has singularities. We are confronted here with a drastically new concept that during the time evolution of a massive star a space-time region is created which is excluded from the physical scene, being physically unreachable by test particles or observables. If this concept is accepted, then it seems plausible that the gravitational singularities are excluded from the modified theory.