The Israel Theorem: What is Nature Trying to Tell Us?

We explore the possible physical consequences derived from the fact that the only static and asymptotically-flat vacuum space-time possessing a regular horizon is the Schwarzschild solution (Israel theorem). If small deviations from the Schwarzschild metric are described by means of exact solutions to Einstein equations (as it should be), then for very compact configurations, at the time scale at which radiatable multipole moments are radiated away, important physical phenomena should occur, as illustrated by some results on different solutions beloging to the Weyl class of static axially--symmetric solutions to the Einstein equations.