An alternative approach to the static spherically symmetric vacuum global solution to the Einstein's equations

Abstract: We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution be static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of signature implying a complex transformation of an angle variable. There is a "phase transition" on the surface R=2m, producing a change in the symmetry as we cross this surface. Some consequences of this situation on the motion of test particles are investigated.