Black holes in many dimensions at the LHC: testing critical string theory

We consider black hole production at the LHC in a generic scenario with many extra dimensions where the Standard Model fields are confined to a brane. With $\sim 20$ dimensions the hierarchy problem is shown to be naturally solved without the need for large compactification radii. We find that in such a scenario the properties of black holes can be used to determine the number of extra dimensions, $n$. In particular, we demonstrate that measurements of the decay distributions of such black holes at the LHC can determine if $n$ is significantly larger than 6 or 7 with high confidence, and thus can probe one of the critical properties of string theory compactifications.