Four-stage workflow · BZ + superradiance + Hawking + total compute budget

Black Hole Energy Budget

Two routes to extract energy from a spinning black hole — BZ magnetic coupling and superradiant boson amplification — and one inescapable drain: Hawking evaporation. This workflow runs all three and sums the compute budget over the IMBH lifetime.

🔬 Established GR/MHD/QFT ⚠ Ultralight boson (Stage 2) ✦ MTH compute application

No backend · No tracking · State in URL hash · v1.0 · 2026-06-01

Blandford-Znajek 1977 · Tchekhovskoy et al. 2010

BZ Power — Magnetic Energy Extraction

Set IMBH mass, spin, and magnetic field to get BZ jet power

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The Blandford-Znajek process couples magnetic field lines threading the event horizon to the hole's rotation, extracting rotational energy as a Poynting-flux jet. Power scales as P_BZ ∝ B² M² a². Mass and spin are also passed forward to Stages 2, 3, and 4 — they are the shared substrate parameters for all subsequent calculations.

Inputs

IMBH mass M (M☉)

30,000 M☉

Spin a*

a* = 0.900

Magnetic field B at horizon (T)

10⁶ T

Stage 1 outputs

BZ power P_BZ—W

Kardashev K—

vs. solar luminosity—

Penrose extractable fraction—

Horizon radius r₊—km

→Passes to all stages: M = —, a* = —, P_BZ = —

Press & Teukolsky 1972 · Detweiler 1980

Superradiance — Wave Energy Extraction

Alternative channel: ultralight boson amplification around the horizon

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Superradiance is the wave-field analogue of BZ: a massive bosonic field (axion, dark photon) resonates around the spinning hole when the superradiance condition ω < mΩ_H is met, exponentially growing a "cloud" that drains angular momentum. For an ultralight boson of mass μ, the gravitational fine-structure constant α = GMμ/ℏc³ determines the growth rate. M and spin are inherited from Stage 1.

Inputs (M, a* from Stage 1)

M, a* from Stage 1—

Boson mass μ (eV) — log₁₀

10⁻¹⁴·² eV

Stage 2 outputs

α (grav. fine-structure const.)—

Superradiance condition—

e-folding time τ—

Cloud energy (≈5% Mc²)—J

vs. BZ (comparative channel)—

→Note: superradiance spins the hole down — passes updated effective spin to Stage 3's lifetime calc

Hawking 1974 · M³ evaporation scaling

Hawking Evaporation — Lifetime Budget

The substrate's lifetime: how long before it evaporates?

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Every black hole is losing mass to Hawking radiation — at a rate so slow for an IMBH that it's irrelevant on civilisational timescales, but crucial for comparing the substrate's total energy budget to any alternative. The evaporation time t_evap ∝ M³ means even 8,200 M☉ lasts ~10⁷⁹ years. M is inherited from Stage 1.

Inputs (M from Stage 1)

M from Stage 1—

Stage 3 outputs

Hawking temperature T_H—K

Hawking luminosity P_H—W

Evaporation time t_evap—

t_evap vs. stellar epoch end—

t_evap vs. proton decay—

Rest-mass energy Mc²—J

→Passes to Stage 4: t_evap = — · total energy = Mc² = —

Bekenstein-Landauer-Lloyd · total ops over t_evap

Total Compute Over IMBH Lifetime

How many operations can be performed before the BH evaporates?

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With BZ power (Stage 1) and evaporation lifetime (Stage 3) both known, this stage computes the total ops over the IMBH's life. The Landauer floor determines ops/joule; multiplied by Mc² gives the total budget. This is the ceiling on what the MTH civilisation can ever compute — and it is astronomical.

Inputs (P_BZ from S1, t_evap and Mc² from S3)

P_BZ—

t_evap—

Mc² (total energy budget)—

Operating temperature T (K)

2.73 K (CMB)

Stage 4 outputs — lifetime totals

Landauer ops/second—

Lloyd ops/second—

Total ops over lifetime (Lloyd)—

vs. Earth silicon (lifetime)—

✓ Black Hole Energy Budget — Full Summary

BZ power P_BZ

—

watts

Superradiance τ

—

e-folding time

Hawking lifetime

—

years

Total compute (lifetime)

—

ops (Lloyd bound)

—

Full tools: BZ / Kardashev Superradiance Hawking Evaporation B-L-Lloyd Scenario