Demo · MTH Engineering

Spin-Up Economics: Is Phase 1 Viable?

Four tools chain from stellar capture rate to BZ power output — quantifying the Phase 1 engineering timeline and identifying the bottleneck.

4 tools · ~20 min · OCS Phases 1–3
⚙ Choose an accretion regime

Phase 1 spin-up takes very different amounts of time depending on whether the IMBH accretes only from natural tidal captures or from an actively managed feeding programme. Select a scenario to load all four tools with matching parameters.

01
Step 1 · Fuel Supply
The Capture Rate Sets the Clock

Phase 1 of the MTH plan requires spinning up the IMBH via accretion from the ISCO. The fuel comes from stars that wander within the tidal capture radius. In OC’s current core density, the tidal capture rate is estimated at ~10−³ M⚁/yr — roughly one 1 M⚁ star every thousand years. This is the natural rate set by two-body relaxation in OC’s core. Phase 2 involves active stellar deflection to increase this rate by two orders of magnitude, but that requires pre-existing civilisational infrastructure — which itself requires Phase 1 to have been completed first. Natural accretion is therefore the only bootstrapping pathway.

Open Tidal Capture Calculator → mass=8200 Newtonian dynamics
Step payoff
The tidal capture rate is the fundamental clock speed of Phase 1. It is set by OC’s observed core density — a measured quantity — not a free parameter.
02
Step 2 · Mass Accumulation
How Much Mass Is Needed?

To spin up from a★ = 0 to 0.95 requires accreting ~38% of the initial mass — for a starting mass of 8,200 M⚁, that’s ~3,100 M⚁. This is the Thorne (1974) spin-up formula: a thin accretion disc at the ISCO is maximally efficient at angular momentum transfer. At 10−³ M⚁/yr, this takes 3.1 billion years — roughly 25% of OC’s remaining lifetime. Phase 2 feeding at 0.1 M⚁/yr reduces this to 31,000 years. The IMBH growth history tool shows how mass and spin evolve together along this trajectory, accounting for the changing ISCO radius as spin increases.

Open IMBH Growth History → M=8200 · initial spin=0 · target a★=0.95 Thorne 1974
Step payoff
The mass budget is fixed by the Thorne formula. ~3,100 M⚁ is the price of Kardashev II. The timeline question is entirely about how fast that mass can be delivered.
03
Step 3 · The Timeline
From Zero to Kerr-Maximal

The spin-up calculator integrates the Thorne (1974) formula: mass accreted to reach spin a★ from rest scales as 1 − √(rISCO(a★)/6). The Phase 1 bottleneck is not physics — it is the accretion rate. At natural capture rates (Scenario A), Phase 1 requires ~3 Gyr. At Phase 2 feeding (Scenario B), it compresses to ~31,000 years. But the BZ power at the END of Phase 1 is ~4×10³⁵ W — enough to run Phase 2 active feeding at minimal energy cost. The two scenarios converge on the same endpoint: a★ = 0.95, M = 11,300 M⚁, Kardashev K ≈ 2.49.

Open Spin-Up Timeline → M=8200 · a0=0 · af=0.95 · &Mdot;=10−³ M⚁/yr Thorne 1974 MTH Phase 1
Step payoff
3 Gyr is long by human standards but short compared to OC’s ~10 Gyr remaining lifetime. Phase 1 is feasible on natural timescales if any technological civilisation emerges in OC in the next ~7 Gyr.
04
Step 4 · The Payoff
BZ Power at the End of Phase 1

After spin-up to a★ = 0.95 with a final mass of ~11,300 M⚁ (8,200 + 3,100 accreted), the BZ power at B = 10&sup6; T is P_BZ ≈ 8.4×10³⁵ W. This is Kardashev K ≈ 2.49 — solidly Kardashev II. Both scenarios arrive at the same BZ endpoint because they accrete the same total mass to the same final spin; they differ only in how long that journey takes. The argument is self-consistent: once started, the IMBH’s own energy output can sustain and accelerate Phase 2. The BZ power exceeds the energy cost of active feeding by many orders of magnitude.

Open BZ Calculator → mass=11,300 M☉ · spin=0.95 · B=10⁶ T Blandford-Znajek 1977 MTH Phase 2 entry
Step payoff
P_BZ ≈ 8.4×10³⁵ W is the Phase 1 graduation certificate: a power source large enough to fund everything that follows. Kardashev II is not a destination, it is the key to Phase 2.
⚖ Self-Consistent Bootstrap

Natural accretion (Scenario A) makes Phase 1 viable on a billion-year timescale — expensive in time, but feasible within OC’s remaining lifetime. Phase 2 feeding (Scenario B) compresses the timeline dramatically but requires prior civilisational infrastructure — which itself requires Phase 1 to have been completed. This is not circular: any civilisation that reaches modest Type I technology could begin Phase 1 on natural timescales, then use the resulting BZ power to accelerate Phase 2 for subsequent civilisations.

The critical insight: the spin-up economics are self-consistent. The BZ power at Phase 1 completion (~4×10³⁵ W under Phase 1 conditions, ~8.4×10³⁵ W at final mass) exceeds the power required for Phase 2 active feeding by many orders of magnitude — the system bootstraps itself. The MTH plan does not require solving the energy problem first; it requires only waiting.

For the reconnection contribution on top of BZ at the Phase 1 endpoint, see Demo — Reconnection vs. BZ. For the full extraction sequence including Phases 2 and 3, see the BH Energy Budget Workflow.

EPISTEMIC TIERS: Established = peer-reviewed physics within the standard formulation. Debated = active disagreement in the published literature. Theoretical = published framework, awaiting decisive observation.