  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.
