  We study the effect of primordial black holes on the classical rate of
nucleation of AdS regions within the standard electroweak vacuum. We find that
the energy barrier for transitions to the new vacuum, which characterizes the
exponential suppression of the nucleation rate, can be reduced significantly in
the black-hole background. A precise analysis is required in order to determine
whether the the existence of primordial black holes is compatible with the form
of the Higgs potential at high temperature or density in the Standard Model or
its extensions.
