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Protons are composite particles, with a radius of about 10^-15 m = 1 femtometer = 1 fm

Quarks and leptons (electrons, neutrinos) are hypothetically non-composite and point-like.

Subatomic nature of solid matter: Most matter at the sub-femtometer scale is empty space with a distribution of relativistic fermions.

All fundamental fermions (quarks, leptons, etc.) have an angular momentum of h/4π (or 3h/4π if you assume SUSY).

GR Schwarzschild black holes are non-rotating. They have radius r_{Schwarzschild} = 2Gm/c²

Black holes work by a central force, so they conserve angular momentum. This mean they do not hoover up star systems, but are sloppy, inefficient eaters at best. For a GR black hole, the capture cross-section for relativistic particles is a small multiple of the geometric cross-section: σ = πkr² = 4πkG²m²/c^4

The rate at which a sub-femtometer scale black hole consumes the Earth can be closely approximated by treating it as carving a cylinder. For a Earth of approximate diameter, 2 r_{Earth} = 1.27×10^7 m, density D = 8000 kg/m³, and ½ LEO period, T=44 minutes, we can compute the rate of mass consumption as D(2 r_{Earth})σ/T

This rate is highly optimistic since even a small non-zero motion relative to Earth's center will cause the period to increase and the chord of Earth to be a non-diameter.

GR can't be the end-all to black hole physics, since GR has no quantum effects.

Effect one: Hawking evaporation

According to Hawking, black holes lose mass due to evaporation at a rate of hc^4/(30720π²G²m²)

This means they have a lifetime of 92160π²G²m³/(hc^4)

This also means that there is a minimum mass, below which the black hole evaporates faster than it gains, m_0 = (c²/G) ((2640 s) h/(245760π³k(8000 kg/m³)(1.27×10^7 m)))^(1/4)

Effect two:

Black holes with too much angular momentum aren't black anymore (they are naked singularities). This limit on angular momentum is related to mass. Just below the Planck mass is a mass where a spin-less black hole cannot absorb a fermion without losing it's black-ness. This means that for smaller black holes, their capacity to absorb matter must be severely reduced from the non-quantum estimates.

LHC throws protons together with a center-of-mass mass-energy of about 14 TeV, but the interesting collisions are the quark-quark collisions which are designed to happen with a center-of-mass mass-energy of 2 TeV.

There is no records of collider experiments producing products with zero velocity in the lab frame. Since most products are highly relativistic, a crude estimate of quark-quark center-of-mass velocities < 10^-5 c is 0.001% which is 2 orders of magnitude less than Walter Wagner's lowest estimate.

LHC has a planned luminosity of 10^38/m²s so that events with a cross-section of less than about 3×10^-51 m² have less than even odds of being seen in a billion years of continuous LHC operation. For comparison, a 2 TeV GR Black Hole has a cross-section of about 10^-100 m²

A hypothesis with as yet no experimental data, called XLD, for Extra Large Dimensions, speculates that 2 TeV black holes might have a radius larger than the 5.30×10^-51 m predicted by GR, with correspondingly larger cross-section. XLD does have Hawking evaporation, as its authors started with quantum theory to get to XLD. There seem to be no good reason for equating 2 TeV with a XLD black hole radius of 0.0001 fm, except for the publicity reasons that just happens to make the luminosity-cross-section product near the 1 black-hole per second that makes the paper inflaming to the imagination.

Eric has uncritically accepted 2 TeV = 0.0001 fm, which begs the question about growth. It seems obvious that a 0.0001 fm XLD 2 TeV black hole would have far less gravity than a 0.0001 fm GR 67,500 ton black hole, so that the factor k would be exactly 1. It also seems obvious that the XLD-mass-radius curve must approach the GR mass-radius curve so that macroscopic GR (which is observed) is preserved. So XLD black holes must increase in radius very slowly over the 2-TeV to 67,500 ton mass range ( 31 orders of magnitude! ). This means that growth is not geometric, but linear, taking billions of billions of years to grow to 67,500 tons -- if we suppose (as Eric insists) that we discount Hawking evaporation for the trifling reason that we haven't observed it yet. (This is highly inconsistent, since we haven't observed sub-stellar-mass black holes or evidence for XLD, but Eric insists on those.)

So even if LHC makes stable 2 TeV, 0.0001 fm black holes at a rate of 1/second for 1500 years (50 billion black holes), and even if each we produced at exactly zero relative motion relative to Earth's center, over 10 billion years they would only grow to 3.8×10^-13 kg (each) for a total mass of 19 grams of black hole against the Earth's mass of nearly 6×10^24 kg. (Except that even 3.8×10^-13 kg is well below the Kerr limit which keeps tiny black holes from absorbing fermions.)

The problem with risk analysis and Eric, is even when we assume as facts the hypotheses he comes up with, the numbers indicate the risk is actually zero.

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