  We investigate false vacuum decay catalysed by black holes under the
influence of the higher order Gauss-Bonnet term. We study both bubble
nucleation and Hawking-Moss types of phase transition in arbitrary dimension.
The equations of motion of ''bounce'' solutions in which bubbles nucleate
around arbitrary dimensional black holes are found in the thin wall
approximation, and the instanton action is computed. The headline result that
the tunnelling action for static instantons is the difference in entropy of the
seed and remnant black holes is shown to hold for arbitrary dimension. We also
study the Hawking-Moss transition and find a picture similar to the Einstein
case, with one curious five-dimensional exception (due to a mass gap). In four
dimensions, we find as expected that the Gauss-Bonnet term only impacts
topology changing transitions, i.e. when vacuum decay removes the seed black
hole altogether, or in a (Hawking-Moss) transition where a black hole is
created. In the former case, topology changing transitions are suppressed (for
positive GB coupling $\alpha$), whereas the latter case results in an enhanced
transition.
