RELATIVISTIC STABILITY. PART 2: A STUDY OF BLACK-HOLES AND OF THE SCHWARZSCHILD RADIUS

We point out a sufficient condition for existence of a stable attractor in the two-body restricted problem. The result is strictly dependent on making reference to relativistic equations and could not be derived from classical analysis. The radius of the stable attractor equals the well known Schwarzschild radius of General Relativity (GR). So we establish a bridge between Special Relativity (SR) and GR via Stability Theory (ST). That opens one way to an innovative study of black-holes and of the cosmological problem. A distinguishing feature is that no singularities come into evidence. The application of the Direct Method of Lyapunov (with a special Lyapunov function that represents the local energy) provides us the theoretical background.