Re-examines whether the LHC would actually cross into the semiclassical black-hole regime given realistic parton energies, arguing the produced objects are more likely “stringy”/quantum-gravitational states well below the semiclassical (many-times-Planck-mass) regime assumed by Dimopoulos-Landsberg and Giddings-Thomas, which changes decay-signature expectations and bears directly on whether the produced objects behave as calculable, radiating semiclassical black holes at all versus something in the poorly-understood quantum-gravity/remnant end-state regime. relevance_note: directly probes the greybody/quantum-gravity-endpoint soft spot — whether LHC-scale objects are even in the semiclassical regime where the Hawking-evaporation calculation is trustworthy.
§2 Black-hole production and decay
O-20 - LHC parton luminosities fall steeply with invariant mass, concentrating any threshold process just above threshold
A firmly established property of the measured proton PDFs (external global-fit data, not this paper’s own measurement), used throughout the paper: it is why the black-hole/strong-gravity event sample at the LHC would sit at the lowest accessible mass scale rather than well above threshold.
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A-11 - Thermality criteria require black-hole masses several times the Planck scale, out of reach of near-threshold LHC production
Reasoning (each step is a calculation in the paper; xmin ≡ MBH/M measures how far above the relevant Planck scale M the object sits):
- Convention ambiguity: the Planck scale M is convention dependent (Dimopoulos-Landsberg vs PDG vs RS normalizations differ by factors of ~1.6-2.9 in the implied threshold), so E > M is necessary but nowhere near sufficient, and quoted “black holes at ~1 TeV” claims are convention-laden.
- Compton-wavelength criterion: requiring a colliding quantum of energy E/2 (wavelength 4π/E) to fit inside the Schwarzschild radius of a black hole of mass E gives xmin > 4.1 for ADD n=6 and xmin > 16 for RS1 (weaker variant rS > 1/E still gives 0.44 and ~3 respectively).
- Thermodynamic criteria: |∂T/∂M| ≪ 1 (equivalently large entropy, satisfied already near xmin ~ 1); every degree of freedom carrying energy ≪ MBH, i.e. (n+3)T < M, satisfied only for xmin ≳ 2, and a single bulk mode carries essentially all the energy at MBH ~ 2-3 M; lifetime τ > 1/M needs xmin ~ 1.3 (ADD) / 1.6 (RS); τ > rS (re-equilibration during brane decay) needs xmin ≳ 3 (ADD).
- Entropy/multiplicity: at the maximum experimentally reachable xmin (~6 for ADD n=6, ~10 for RS) the corresponding thermal state would consist of only ~3-6 quanta sharing the energy - inadequate for anything “thermal”; ⟨N⟩ > 2 already requires MBH > 1.5 MD (ADD) or > 4 M̃ (RS).
- All criteria should really hold with margin (≫1, not ~1); but by the falling parton luminosities (the attached observation), production at such xmin is rate-suppressed below observability, while what is actually produced sits at the lowest allowed mass. Hence the highly studied thermal multiparticle signatures are unrealistic, and earlier analyses using low or no xmin overstate the semiclassical character of LHC objects.
Validity verdict (step 6)
Reconstruction: premises = the per-criterion xmin calculations and the attached observation (steeply falling parton luminosities); conclusion = what the LHC would actually produce sits near threshold and fails the thermality criteria. Load-bearing step: each criterion is a necessary condition, so trustworthy thermality needs the max of the xmin values (~3-16, with margin); steep luminosity fall means production is dominated by the lowest allowed mass while high-xmin production is rate-suppressed. Traced this combination - it is a straightforward conjunction-plus-monotonicity argument. Undercutting probe: none survives conditional on the premises; whether the individual xmin numbers are right is premise-truth for steps 7-8.
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A-12 - Collisional inelasticity leaves only a fraction of parton energy behind the horizon, cutting black-hole cross sections by orders of magnitude
Reasoning:
- Define inelasticity y ≡ MBH/√ŝ. The energy not trapped behind the apparent horizon is radiated gravitationally in the collision; classical results (from Penrose / D’eath-Payne in 4D, extended to higher D and nonzero impact parameter by Eardley-Giddings and refined by Yoshino et al.) give y ≲ 0.6 at b=0 for both the 10D (ADD) and 5D (RS) cases, falling with b - to y ≈ 0 (ADD) and y ≈ 0.2 (RS) at the largest horizon-forming impact parameter.
- To make a black hole of mass MBH one therefore needs parton energies larger by 1/y; because parton luminosities fall steeply, the impact-parameter-averaged cross section (eq. 2.21, weighting by 2z dz with z = b/bmax and threshold (xmin MD)²/(y(z)² s)) drops by orders of magnitude versus the geometric estimate (Figure 4), more strongly for ADD than RS.
- These classical y values are lower bounds computed near the Planck scale where quantum-gravity corrections are unknown - one more way the naive production picture is unreliable near threshold.
- Together with the thermality thresholds, this pushes genuinely semiclassical production even further out of the LHC’s effective reach.
Validity verdict (step 6)
Reconstruction: premises = classical trapped-surface inelasticity values (y <~ 0.6 at b=0, falling with b) and steeply falling parton luminosities; conclusion = impact-parameter-weighted cross section falls orders of magnitude below the geometric estimate. Traced the load-bearing step: making mass MBH requires parton CM energy MBH/y, and a steeply falling luminosity evaluated at higher invariant mass suppresses the rate by orders of magnitude; averaging over b with y(b) decreasing only strengthens this. Valid conditional on the y values; their classical near-Planck provenance is flagged in the body and priced downstream.
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§3-5 Decays, two-body final states, conclusions
H-14 - LHC strong-gravity objects would be near-threshold quantum or stringy states, not semiclassical thermal black holes
Consequence drawn in the paper: expected decays are low-multiplicity (typically two-body) final states rather than isotropic high-multiplicity “fireballs”, and near-threshold behavior is governed by unknown quantum gravity rather than by the calculable semiclassical formulae.
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H-15 - The first observable low-scale quantum-gravity signature at the LHC would be enhanced transverse two-body final states
The two-body threshold is argued to sit almost inevitably below the true (thermal) black-hole threshold, and the energy dependence and angular distribution (Rη) of the two-body excess could distinguish black-hole-like cross sections, perturbative string resonances, and higher-dimension operators.
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