Introduction
In 1921, while Einstein and his followers were baffled by the existence of a singularity at the horizon in the Schwarzschild spacetime, looking spoiling the consistency of the Einstein theory, Painlevé proposed a solution which discarded the singularity.
Totally misunderstood at that time and rejected because it included a non-quadratic term in the metric, which is, in fact, mandatory in these coordinates for allowing this non-symmetrical phenomenology of this horizon, his proposal felt into oblivion for about 80 years before being rediscovered, in its full beauty.