Build a Kardashev-III

Every calculation that follows depends on the IMBH mass. Start by seeing how constrained that mass actually is. The constraint stacker shows every published measurement — kinematic, proper-motion, timing, accretion, N-body, and M–σ — in a single plot. For the Häberle and Bañares scenarios, the tension between ≥ 8,200 and ≤ 6,000 M⊙ will be visible; for Sgr A*, the mass is known to better than 0.5% and the window is essentially a vertical line. The mass uncertainty propagates into every downstream number in this demo.

A rotating black hole carries rotational energy in its ergosphere that can be extracted electromagnetically via the Blandford–Znajek (BZ) mechanism. A poloidal magnetic field threading the horizon drives a Poynting flux that can be coupled to external loads. For an 8,200 M⊙ IMBH at spin a = 0.7, the BZ power scales as P_BZ ≈ 4×10³⁷ W × (B/10⁶ T)². At magnetar-surface fields (B ≈ 10⁸ T), P_BZ ≈ 10⁴¹ W; reaching Kardashev-III (4×10³⁷ W) requires B ≈ 10⁶ T. Fields of 100 G (10^-2 T) give only ~10²¹ W — the slider lets you explore the full range. The tool's inverse mode shows the spin required to achieve a target power level.

The Bekenstein–Landauer principle sets the minimum energy cost per bit erasure: E ≥ k_BT ln 2. Near a black hole, the relevant temperature is the Hawking temperature T_H ≈ 6 × 10&sup6; K for an 8,200 M⊙ BH — much colder than the surface of a star, meaning the energy cost per bit is correspondingly lower. The Bekenstein bound on information content also provides an absolute upper limit on the number of bits encodable in a given volume near the horizon. The combination means that the ergosphere is a maximally efficient compute medium in the thermodynamic sense: low temperature, huge Bekenstein capacity, relativistic time dilation (Step 4).

Clocks near a massive object run slower than clocks far away — a direct consequence of the equivalence principle. Infrastructure stationed at r = 2.5 r_s (just outside the ISCO for a Schwarzschild BH) experiences a time dilation factor of ≈ 10×. In a rotating Kerr spacetime the ISCO is dragged inward: r_ISCO ≈ 1.3 r_s at a = 0.7, pushing the dilation factor to ≈ 30×. This is a computable “slow-time” dividend: for every second that passes in the Galaxy at large, 30 seconds of compute-local time pass near the horizon. The total operation count (Step 6) is multiplied by this factor.

Hawking radiation causes black holes to slowly evaporate. For an 8,200 M⊙ BH, the evaporation timescale is t_evap ≈ 10&sup8;&sup4; yr — the universe is 10¹° yr old by comparison. Hawking radiation is not the limiting factor for civilisational planning. However, the BZ power extraction also extracts angular momentum and mass from the BH. At a sustained extraction rate of 10³&sup6; W from 8,200 M⊙, the spin-down timescale is t_BZ ≈ 10¹³ yr — still enormously long, but finite and relevant for planning the operational horizon of the infrastructure.

Multiply: BZ power (Step 2) × time-dilation factor (Step 4) × BZ operational horizon (Step 5) ÷ energy per operation (Bekenstein–Landauer floor, Step 3). For ω Cen at 8,200 M⊙, the result is a total operation count of order 10¹³&sup6; operations over the BZ lifetime — more than 10&sup5;&sup0; times the estimated total operations performed by all human computing hardware in history. This is the quantitative argument behind the Macro Transcension Hypothesis: settlement near an IMBH, not stellar colonisation, maximises cumulative civilisational compute. Use the tool to explore how this changes with mass, spin, radiator temperature, and duty cycle.