Scenario · macro transcension hypothesis · chains six tools

Build a Kardashev-III

Six tools quantify what a civilisation could do if it settled near ω Cen's intermediate-mass black hole: Blandford–Znajek power extraction, Bekenstein–Landauer information limits, deep gravitational time dilation, Hawking evaporation timescale, and total civilisational compute budget.

No backend · No tracking · Works offline · v1.0 · 2026-05-28
⚙ Choose the black hole

The compute budget scales strongly with BH mass and spin. Three scenarios span the observational uncertainty for ω Cen's IMBH and include Sgr A* as a galactic-centre reference point.

01
Tool 2 · all published constraint families
First: how confident are we in the BH mass?

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.

Open Constraint Stacker → Debated Mass constraint
Step payoff
At 8,200 M⊙ the BZ power is 1.87× that at 6,000 M⊙, since P ∝ M²; the lifetime operation budget (Step 6) is 1.37×, since the extractable reservoir ηMc² scales only as M. The mass question matters enormously for the quantitative argument.
02
Tool 3 · Blandford–Znajek process — Kardashev scale
BZ power extraction: tapping the ergosphere

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 PBZ ≈ 4×1037 W × (B/106 T)². At magnetar-surface fields (B ≈ 108 T), PBZ ≈ 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 fixes a target power and solves for the magnetic field required, holding mass and spin.

Open BZ Kardashev → Theoretical Kardashev-III
Step payoff
P_BZ ≈ 1036 W at 8,200 M⊙, a=0.7. The BZ process is observationally confirmed in AGN jets; the extrapolation to a civilisational power infrastructure is the speculative leap.
03
Tool 23 · Bekenstein–Landauer limits — BH thermodynamics
Information limits near the horizon

The Bekenstein–Landauer principle sets the minimum energy cost per bit erasure: E ≥ kBT ln 2. Near a black hole, the relevant temperature is the Hawking temperature TH ≈ 6 × 106 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).

Open Bekenstein–Landauer → Thermodynamics Holographic bound
Step payoff
T_H at 8,200 M⊙ is ≈ 7.5×10-12 K — far below the 2.7 K CMB, making Hawking radiation undetectable. The energy per bit floor is correspondingly low, and the horizon encodes A/(4 lp² ln 2) = 1.0×1085 bits.
04
Tool 4 · Schwarzschild–Kerr metric — gravitational time dilation
Slow-time computing: the relativistic bonus

Clocks near a massive object run slower than clocks far away — a direct consequence of the equivalence principle. Infrastructure stationed at r = 2.5 rs sits just inside the Schwarzschild ISCO at 3 rs = 6 rg, so holding that radius needs station-keeping; the static factor there is 1/√(1 − 1/2.5) = 1.29×. In a rotating Kerr spacetime the ISCO is dragged inward to rISCO = 3.39 rg = 1.70 rs at a = 0.7, where an orbiting clock runs 1.91× slower than a distant one. Deeper stationing slows the local clock rather than speeding it up. 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.

Open Time Dilation → GR Civilisational
Step payoff
At r=2.5 r_s around an 8,200 M⊙ BH the static time-dilation factor is 1.29×, and a station orbiting at the prograde ISCO (a=0.7) runs 1.91× slower than a distant clock. The dividend is that external epochs pass cheaply, not that local computation runs faster, and at these radii the factor is about two rather than thirty.
05
Tool 14 · Hawking radiation — lifetime and power budget
How long does the substrate last?

Hawking radiation causes black holes to slowly evaporate. For an 8,200 M⊙ BH, the evaporation timescale is tevap = 1.2×1079 yr, against a universe 1.4×1010 yr old. Hawking radiation is not the limiting factor for civilisational planning. However, the BZ power extraction also extracts angular momentum and mass from the BH. The extractable rotational reservoir at a = 0.7 is ηmaxMc² = 0.0742 × 1.47×1051 J = 1.09×1050 J, so a sustained 1036 W draw exhausts it in tBZ = 3.4×106 yr. Spin-down, not evaporation, sets the operational horizon, and it is 73 orders of magnitude shorter.

Open Hawking Evaporation → QFT / semiclassical Lifetime limit
Step payoff
Evaporation time 1.2×1079 yr is irrelevant to engineering. The BZ spin-down horizon at a sustained 1036 W is 3.4×106 yr, far short of the current age of the universe, which sets the operational planning envelope.
06
Tool 9 · compute-in-space — BZ power source — total operation budget
The total civilisational compute budget

The product of BZ power (Step 2) and the operational horizon (Step 5) is simply the extractable rotational reservoir, ηmaxMc² = 1.09×1050 J at 8,200 M⊙ and a = 0.7. Divide by the Landauer floor kBT ln 2 to get the operation count. Against today's 2.73 K CMB that floor is 2.6×10−23 J, giving 4.2×1072 operations; aestivating to 10−9 K lowers the floor to 9.6×10−33 J and raises the total to 1.1×1082 operations. Time dilation does not enter this product: it redistributes when the operations happen, not how many the energy budget can buy. 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.

Open Compute in Space → Speculative MTH
Step payoff
Total operations 4.2×1072 at 8,200 M⊙ against the present CMB, or 1.1×1082 after aestivation to 10−9 K. At 6,000 M⊙ the figures are 3.1×1072 and 8.3×1081: the reservoir scales as M, so the mass tension costs a factor of 1.37 here even though it costs 1.87 in power.
▸ The Macro Transcension Hypothesis, quantified

The Macro Transcension Hypothesis (Smart 2012, as developed in the OCS context) argues that intelligent civilisations that optimise for compute density will converge on the vicinity of rotating black holes rather than expanding outward through stellar space. This demo shows the quantitative case: BZ power at 1036 W, Bekenstein–Landauer compute efficiency near the cold Hawking temperature, and an operational horizon of 1013 yr give a total compute budget that exceeds any stellar-expansion trajectory by many orders of magnitude.

The chain is fully grounded in established physics through Step 4 (general relativity). Step 5 (Hawking radiation) is semiclassical QFT — established but not yet confirmed for astrophysical black holes. Step 6 (civilisational extrapolation) is speculative but physically motivated extrapolation, not fantasy: every quantity is derived from a published formula, and the tool allows you to vary every assumption.

The observational predicate remains the IMBH itself. See Demo A — Is There an IMBH? for the six-tool evidence tour. See Demo O — Fermi Five Ways for the broader Fermi-paradox context in which the MTH is one of five candidate resolution mechanisms. The decision tree at Demo M maps how these lines of evidence interact.

WANT THE LIVE CASCADE VERSION?   ⚡ MTH Compute Budget workflow — same argument, but every stage output feeds the next stage's input automatically in a single page.

EPISTEMIC TIERS: Established = peer-reviewed physics within the standard formulation. Debated = active disagreement in the published literature. Theoretical = published framework, awaiting decisive observation. Speculative = physically motivated extrapolation, not yet observationally constrained.