1Feeding Rate 2Spin-Up Timeline 3BZ Power 4Orbit Positioning Summary
Four-stage MTH chain · accretion → spin-up → BZ power → orbital positioning

From Feeding Rate to Engineering-Ready Spin

The MTH engineering chain: given OC's IMBH current accretion state, how long until it reaches an engineering-viable spin? Then: what BZ power becomes available, and where would you park a computation substrate?

🔬 Bondi + Kerr physics (stages 1–3) ✦ MTH application (stage 4)
Refs: González Prieto 2025 · Thorne 1974 · Blandford & Znajek 1977 · Smart 2012 · v1.0 · 2026-06-03
01
Bondi–Hoyle accretion · González Prieto et al. 2025
Current Feeding Rate

OC's IMBH is currently in a quiescent/sub-Eddington accretion state with no detected radio or X-ray counterpart. The Bondi–Hoyle rate from the ambient stellar winds and ISM in OC's core sets the mass inflow. Only a fraction F_Bondi actually reaches the horizon.

Inputs
8,200 M☉
1.0 cm⁻³
0.030
Stage 1 outputs
Accretion rate ṁaccM☉/yr
Eddington fraction λ
Accretion mode
Mass gain in 1 MyrM☉
acc = M☉/yr · λ =
02
Thorne 1974 · prograde disc spin-up
Spin-Up Timeline

Prograde disc accretion spins up the IMBH toward the Thorne limit (a★ = 0.998). The spin-up mass fraction is ΔM/M = 1 − √(r_ISCO(a★)/6). At the current quiescent accretion rate, this takes an astronomically long time without engineering assistance.

Inputs (ṁ_acc from Stage 1)
a★₀ = 0.10
a★ = 0.900
ε = 0.100
Stage 2 outputs
Mass needed ΔM (natural)M☉
Time to reach a★targetyr
Verdict vs. cluster dissolution
a★target = · Time = yr
03
Blandford–Znajek 1977 · ergospheric power extraction
BZ Power at Target Spin

At the target spin, the BZ mechanism extracts rotational energy electromagnetically. Power scales steeply: P_BZ ∝ B² M² a². The horizon magnetic field is constrained from below by the current accretion rate.

Inputs (M_BH, a★_target from Stages 1–2)
10⁶ T
Stage 3 outputs
BZ power PBZW
Kardashev scale K
vs. Solar luminosity
PBZ = W · K =
04
✦ MTH application · Smart 2012
Optimal Computation Orbit

With engineering-viable spin achieved, a computation substrate orbiting the IMBH at the ISCO (or slightly outside) experiences gravitational time dilation — more subjective computation time per external year. The ISCO radius and time-dilation factor are fixed by the target spin.

ISCO geometry at a★target
rISCOrg
rISCO physicalkm
Time dilation γ at ISCO
Subjective years per Gyrproper yr/Gyr
Orbital period at ISCO

The time dilation factor γ at r_ISCO means that for every year experienced locally by a near-ISCO substrate, γ years pass at infinity. This is the core MTH efficiency argument: the same computation resources deliver γ× more subjective experience per external year compared to a distant substrate.

At a★ = 0.998 (Thorne limit), r_ISCO ≈ 1.24 r_g and γ ≈ 4.5. At a★ = 0.9, r_ISCO ≈ 2.32 r_g and γ ≈ 1.8.

✓ Accretion → Spin Summary
acc
M☉/yr
Spin-up time
years
PBZ
watts
γ at ISCO
dilation factor

Computing…