Gravity and the Stability of the Higgs Vacuum.

We discuss the effect of gravitational interactions on the lifetime of the Higgs vacuum where generic quantum gravity corrections are taken into account. Using a "thin-wall" approximation, we provide a proof of principle that small black holes can act as seeds for vacuum decay, spontaneously nucleating a new Higgs phase centered on the black hole with a lifetime measured in millions of Planck times rather than billions of years. The corresponding parameter space constraints are, however, extremely stringent; therefore, we also present numerical evidence suggesting that with thick walls, the parameter space may open up. Implications for collider black holes are discussed.