  We study non-perturbative instabilities of AdS spacetime in General
Relativity with a cosmological constant in arbitrary dimensions. In this simple
setup we explicitly construct a class of gravitational instantons generalizing
Witten's bubble of nothing. We calculate the corresponding Euclidean action and
show that its change is finite. The expansion of these bubbles is described by
a lower-dimensional de Sitter geometry within a non-compact foliation of the
background spacetime. Moreover we discuss the existence of covariantly constant
spinors as a possible topological obstruction for such decays to occur. This
mechanism is further connected to the stability of supersymmetric vacua in
string theory.
