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Bentley MoonAn independent commonsFuturism Institute

Research · Blackhole lab

Collapse, Hawking radiation, analog horizons and islands

Four parts of black-hole physics the lab rebuilt from scratch, checked against published values before using them as tools.

Critical collapse

  • At the threshold where collapsing matter just forms a black hole (Choptuik’s critical collapse), the lab reproduces the scaling exponent γ = 0.37396 ± 0.00005 and the echoing period Δ = 3.4453 ± 0.0003, universal to 3e-6.verified · known
  • The maximum of 2m/r on the critical solution is 0.53284, its first explicit value.verified · narrow

Hawking radiation

  • Page’s two budgets for an evaporating black hole reproduced to every quoted digit: 81.4% of the energy leaves as neutrinos when they are treated as massless (Page 1976), and with only photons and gravitons the Page time (when the radiation starts carrying information out) falls at 53.81% of the lifetime (Page 2013).verified · known
  • Area laws reproduced; κ = 0.2954.verified · known

An analog horizon

  • In a Bose–Einstein condensate (a gas cooled until its atoms move as one quantum wave) flowing faster than its own speed of sound, a sonic horizon forms. The correlation between Hawking partners appears in two independent methods, and the spectrum is thermal at κ/2π within 0.44%. The greybody factor at zero frequency, Γ(0), is known.verified · known

Islands

  • Evaporation modelled with Haar-random unitaries (perfectly scrambling random evolutions) equals the fixed-area replica sum, and the island formula (the recent account of how information escapes an evaporating black hole) is its saddle-point limit. The island results reproduce AMM 2019 and PSSY to about 1e-11.verified · known
  • The lab’s part is an error table for the Haar model: the greybody normalisation is 19.5% of S₀; area fluctuations of half a nat against √(2π/β); a missing scrambling delay. Hawking’s original entropy count is excluded after the Page time.ours
Critical collapse: the scaling of black-hole mass near the threshold.
Critical collapse: the scaling of black-hole mass near the threshold.
The Hawking emission spectrum.
The Hawking emission spectrum.
The sonic horizon in a Bose–Einstein condensate.
The sonic horizon in a Bose–Einstein condensate.
Page curves from the island formula and the Haar model.
Page curves from the island formula and the Haar model.
The PSSY model, canonical ensemble, reproduced.
The PSSY model, canonical ensemble, reproduced.

Lab records: H-0013; ledger/notes t3, t4, t7, t5-islands; understanding/09.

Tags: confidence (proved, verified, observed, suggestive, pending) and novelty (known, narrow, ours), defined on the overview.