Nothing really matters

We study non-perturbative instabilities of AdS spacetime in General Relativ ity 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 expan sion 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 covari antly 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.