summary - Analyzes hypothetical stable TeV-scale black holes possibly produced at the LHC, modeling capture and accretion inside Earth, white dwarfs, and neutron stars across a range of extra-dimensional gravity scenarios. Its central move: cosmic rays of far higher center-of-mass energy than the LHC constantly strike white dwarfs and neutron stars, so if slow, stable, LHC-mass black holes could form and grow inside a body, they should already have formed via cosmic-ray impacts on these denser, older, and better-characterized objects. The observed survival of specific catalogued white dwarfs and of the neutron-star population over >=10^8-10^9 yr bounds the accretion/growth rate to values incompatible with disruption, closing the loophole in the naive cosmic-ray argument (that fast, cosmic-ray-produced black holes simply escape Earth) for the slow, trapped case. Concludes “no risk of any significance whatsoever” from such black holes within Earth’s natural lifetime.
relevance_note - The core quantitative safety analysis specifically for stable (non-evaporating) TeV black holes - the scenario that matters if Hawking radiation fails; explicitly extends the shared cosmic-ray-survival premise via independent white-dwarf/neutron-star astrophysical data.
Introduction - the cosmic-ray comparison and its loophole
O-3 - Cosmic rays far above LHC-equivalent energy continuously bombard Earth, white dwarfs and neutron stars
The flux normalization comes from the (contemporaneous) Auger spectrum; the Gyr exposure of astronomical bodies is the shared cosmic-ray survival premise D-1.
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O-4 - Earth and Sun have survived about 4.5 Gyr of ultra-high-energy cosmic-ray bombardment
Directly bounds only scenarios in which cosmic-ray-produced black holes would be stopped inside Earth or the Sun (e.g. charged/EM-interacting black holes); the neutral stable case escapes and needs the WD/NS route.
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H-1 - Stable LHC black holes trapped in Earth would accrete it catastrophically within the solar lifetime
The danger hypothesis G-M set out to test; it presupposes both failure of Hawking evaporation and neutralization/trapping.
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A-1 - Relativistic-escape loophole in the Earth cosmic-ray argument is closed by white-dwarf and neutron-star stopping power
Reasoning
Black holes made by a ~10^17+ eV cosmic ray striking a nucleon at rest inherit large centre-of-mass momentum: typical speeds are near c, vastly above Earth’s 11.2 km/s escape velocity, and a neutral TeV-mass black hole has too small a cross-section to be stopped by Earth’s column density. So the naive argument (“cosmic rays have not destroyed Earth”) has a real loophole for NEUTRAL stable black holes: nature’s versions leave, while LHC pair-production near threshold yields some below escape velocity that stay. G-M close it: white-dwarf interiors (~10^6 g/cm^3) and neutron stars (~10^14 g/cm^3) present column densities sufficient to stop even relativistic TeV black holes produced by cosmic rays impinging on their surfaces. Hence such bodies must have been accumulating trapped stable black holes for >=1 Gyr, and their observed survival bounds the trapped-growth scenario that the LHC could realize on Earth.
Verdict (step 6)
approved / checked. Reconstruction: (P1) cosmic-ray-produced neutral TeV black holes are relativistic and above escape velocity, with cross-sections too small for Earth’s column density to stop — so Earth’s survival cannot bound the trapped-slow case; (P2) WD interiors (~10^6 g/cm^3) and NS (~10^14 g/cm^3) present enough column density to stop even relativistic ones. Conclusion: WD/NS have accumulated trapped stable black holes for >=1 Gyr, so their survival substitutes as the empirical bound. Conditional on P1-P2 the substitution goes through: same object class (neutral stable TeV BH), same trapped end-state, denser host — no undercutting defeater found (the “cosmic rays reach WD surfaces” worry, e.g. magnetic screening, is a premise-truth issue handled by restricting to low-B WDs, priced at step 8, not a validity failure). Elementary kinematics + column-density comparison, traced directly.
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A-3 - Charged or EM-interacting stable black holes are excluded directly by Earth and Sun survival
Reasoning
A charged TeV-scale black hole loses energy by ionization like a heavy charged particle; the stopping length in rock or solar plasma is short, so cosmic-ray-produced charged black holes would have accumulated inside Earth and the Sun over Gyr. Their survival therefore bounds this branch directly. Consequently the only branch needing the white-dwarf/neutron-star argument is the doubly-hypothetical one: Hawking radiation fails AND the black hole sheds all charge (Schwinger discharge), making it neutral and penetrating. This narrows what the overall safety verdict hinges on.
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“If stable black holes retain electric charge (or otherwise interact electromagnetically), ordinary ionization stopping traps even relativistic cosmic-ray-produced ones inside Earth and the Sun, so 4.5 Gyr of survival under the measured cosmic-ray flux directly excludes danger without any white-dwarf step.”
Verdict (step 6)
corrected / checked. The trapping step is valid: conditional on charge retention, ionization stopping of a heavy charged particle in rock/plasma is short-range, so Gyr accumulation inside Earth and Sun follows. But “directly excludes danger” overclaims: an undercutting defeater survives — observer selection (A-6 - Observer selection makes naive survival-based risk bounds uninformative): Earth/Sun survival is conditioned on our existence, so P(we observe survival | dangerous) is not straightforwardly small. The weaker evidential form (“direct evidence against danger for this branch, subject to observer-selection correction”) is immune to the defeater and preserved; the branch-narrowing corollary (only the neutral, Schwinger-discharged branch needs the WD/NS argument) stands unchanged. Statement edited accordingly; filename left as-is per spec.
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Astrophysical anchor bodies
O-1 - White dwarfs of about one solar mass with Gyr ages and low magnetic fields are observed intact
The anchor bodies of the survival bound: dense enough to stop cosmic-ray-produced TeV black holes, old enough that any catastrophic accretion would already have destroyed them. Low magnetic field is required so that incoming UHECR primaries are not deflected/blocked before reaching the surface.
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O-2 - Neutron stars with ages of 100 Myr to Gyr are observed intact
Secondary anchor bodies (density ~10^14 g/cm^3 stops any TeV black hole); the NS bound needs extra assumptions about cosmic rays penetrating NS magnetospheres, so G-M treat white dwarfs as the more robust case.
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Accretion analysis and conclusion
A-2 - Every fast-accretion scenario is excluded by white-dwarf and neutron-star survival
Reasoning
G-M compute Bondi-type accretion rates from first-principles physics across the range of extra-dimensional gravity scenarios (varying the number of dimensions and warping, which set the black hole’s effective capture radius at subatomic scales). The scenarios split into two classes: (1) accretion so slow that Earth suffers no macroscopic effect within the Sun’s natural lifetime - no risk regardless of production; (2) accretion fast enough to matter. In class (2), the same short-distance gravity makes trapped black holes inside far denser white dwarfs and neutron stars accrete those bodies on timescales much shorter than 1 Gyr. Since cosmic rays guarantee production and trapping there (see the stopping-power argument), catalogued >=Gyr-old white dwarfs and old neutron stars would not exist. They do; therefore every class-(2) scenario is empirically excluded, and no scenario is both realizable and dangerous. Caveat load-bearing assumptions: the accretion modelling (contested by Plaga) and cosmic rays actually reaching WD surfaces (low-B WDs) carry the weight.
Verdict (step 6)
approved / checked. Reconstruction: exhaustive two-class bracket on Earth-accretion timescale. Class 1 (slower than macroscopic effect within solar lifetime) is harmless by definition — tautological, valid. Class 2: (P1) the same short-distance gravity that makes Earth accretion fast makes accretion inside far denser WD/NS much faster than 1 Gyr; (P2) cosmic rays guarantee production and trapping in WD/NS (A-1’s conclusion). Then observed >=Gyr-old WD/NS exclude every class-2 scenario. Conditional on P1-P2 the dichotomy is exhaustive and each horn closes, so the inference holds; no undercutting defeater — a scenario dangerous to Earth but slow in a denser body would deny P1 (premise truth, priced at step 8 where Plaga’s accretion-modelling challenge lives), not the inference. Traced the bracketing structure directly.
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H-2 - Stable LHC black holes pose no macroscopic risk to Earth within the solar lifetime
G-M’s conclusion, stated as holding across the full bracket of extra-dimensional scenarios they analyze.
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