  We study the negative modes of gravitational instantons representing vacuum
decay in asymptotically flat space-time. We consider two different vacuum decay
scenarios: the Coleman-de Luccia $\mathrm{O}(4)$-symmetric bubble, and
$\mathrm{O}(3) \times \mathbb{R}$ instantons with a static black hole. In spite
of the similarities between the models, we find qualitatively different
behaviours. In the $\mathrm{O}(4)$-symmetric case, the number of negative modes
is known to be either one or infinite, depending on the sign of the kinetic
term in the quadratic action. In contrast, solving the mode equation
numerically for the static black hole instanton, we find only one negative mode
with the kinetic term always positive outside the event horizon. The absence of
additional negative modes supports the interpretation of these solutions as
giving the tunnelling rate for false vacuum decay seeded by microscopic black
holes.
