Bounds on extra dimensions from micro black holes in the context of the metastable Higgs vacuum

We estimate the rate at which collisions between ultrahigh-energy cosmic rays can form small black holes in models with extra dimensions. If recent conjectures about false vacuum decay catalyzed by black hole evaporation apply, the lack of vacuum decay events in our past light cone may place new bounds on the black hole formation rate and thus on the fundamental scale of gravity in these models. For theories with fundamental scale E∗ above the Higgs instability scale of the Standard Model, we find a lower bound on E∗ that is within about an order of magnitude of the energy where the cosmic-ray spectrum begins to show suppression from the Greisen-Zatsepin-Kuzmin effect. Otherwise, the abundant formation of semiclassical black holes with short lifetimes would likely initiate vacuum decay. Assuming a Higgs instability scale at the low end of the range compatible with experimental data, the excluded range is approximately 1017 eV≲E∗≤1018.8 eV for theories with n=1 extra dimension, narrowing to 1017 eV≲E∗≤1018.1 eV for n=6. These bounds rule out regions of parameter space that are inaccessible to collider experiments, small-scale gravity tests, or estimates of Kaluza-Klein processes in neutron stars and supernovae