Bounds on extra dimensions from micro black holes in the context of the
  metastable Higgs vacuum
  We estimate the rate at which collisions between ultra-high 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 GZK 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 $10^{17} \,\text{eV} \lesssim E_{*} \leq 10^{18.8}\,\text{eV}$
for theories with $n=1$ extra dimension, narrowing to $10^{17}\,\text{eV}
\lesssim E_{*} \leq 10^{18.1}\,\text{eV}$ 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.
