summary - Proposes that the hierarchy problem is solved by n>=2 large compact extra dimensions in which gravity (but not Standard Model fields) propagates, lowering the fundamental Planck scale to as little as ~TeV. This is the enabling premise for the entire micro-black-hole question: without it, LHC collision energies (~14 TeV) sit ~10^15 times below the ordinary 4D Planck scale (~10^19 GeV) and no black hole of any kind is conceivable there. As of the most recent LHC searches (monojet / missing-energy channels), no experimental signature of large extra dimensions has been found; the fundamental scale is now excluded up to roughly 5-10 TeV depending on the number of extra dimensions, i.e. the premise remains speculative but not yet ruled out everywhere.
relevance_note - The speculative pivot the whole question hinges on: TeV-scale gravity is unconfirmed, but the “no risk” conclusion holds either way (no ADD → no BHs at all; ADD true → BHs form but evaporate).
Extracted
O-8 - Electroweak scale lies about 16 orders of magnitude below the observed 4D Planck scale
Link to original
H-3 - Two or more large compact extra dimensions lower the fundamental gravity scale to about a TeV
The enabling premise of the whole micro-black-hole question: if false, LHC energies sit hopelessly below the gravity scale and no BH of any kind forms. Unconfirmed as of the latest LHC monojet/missing-energy searches; fundamental scale excluded up to roughly 5-10 TeV depending on n, i.e. constrained but not refuted.
Link to original
A-4 - Gauss-law dilution of gravity in large extra dimensions reproduces weak 4D gravity from a TeV fundamental scale
reasoning - Gauss’s law in 4+n dimensions with n dimensions compactified at radius R gives M_Pl^2 ~ M_^(2+n) R^n. Setting M_ ~ 1 TeV: n=1 requires R ~ 10^13 cm (solar-system-scale deviations, empirically excluded); n=2 gives R ~ 0.1-1 mm — allowed in 1998, since Newtonian gravity was untested below ~1 mm. So for n>=2 the construction is internally consistent with all then-existing gravity measurements, making a TeV fundamental scale viable rather than obviously excluded. Caveat carried in the paper itself: the radius must be stabilized at the large value, so the hierarchy is relocated rather than dissolved.
Verdict (step 6)
approved / checked. Traced the load-bearing step directly: Gauss’s law in 4+n dimensions gives V ~ 1/(M_^(n+2) r^(n+1)) at r<<R, matching onto 4D Newton at r>>R yields M_Pl^2 ~ M_^(2+n) R^n. Plugging M_* ~ 1 TeV: n=1 gives R ~ 10^13 cm (excluded by solar-system dynamics), n=2 gives R ~ 0.1-1 mm (untested in 1998). So the conclusion — a TeV fundamental scale is consistent with observed 4D gravity for n>=2 — follows, and the statement already carries the honest hedge that the hierarchy is relocated to radius stabilization, not solved. Undimmed by later torsion-balance limits: those bear on premise truth (priced in steps 7-8), not on the inference.
Link to original