An Alternative Approach to the Static Spherically Symmetric, Vacuum Global Solution to the Einstein Equations

We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution is 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.