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

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