Drag the mass slider. Watch the evaporation time race past the age of the universe, past proton decay, past every reference point cosmology can name — and back the other way for primordial black holes that died before the cosmic microwave background formed.
For a Schwarzschild black hole of mass M, in SI units:
T_H = ℏc³ / (8π G M k_B)P_H = ℏc⁶ / (15360π G² M²)t_evap = 5120π G² M³ / (ℏc⁴)
The temperature falls as 1/M, the luminosity as 1/M², and the evaporation time grows as M³ — which is why varying mass on the slider produces such dramatic timeline movement. A factor-of-10 increase in mass moves the evaporation time three decades to the right.
At the low end (~10⁻⁵ kg, micrograms), evaporation is essentially instantaneous — these are hypothetical microscopic black holes from extra-dimension scenarios, not anything astrophysical. At ~10¹¹ kg (~100 million tonnes — small asteroid mass), the evaporation timescale equals the current age of the universe; a primordial black hole of that mass formed in the early universe would be finishing its evaporation right now, producing a final-burst gamma-ray signature that GLAST/Fermi-LAT has searched for and not detected. At stellar masses, the timescale is ~10⁶⁷ years; at supermassive scales, ~10¹⁰⁰ years and beyond. The IMBH preset (8,200 M☉) lands at ~10⁷⁹ years — fifty-five decades past the stellar epoch end, twenty-nine decades past proton decay.
Hawking radiation was derived in 1974 by Stephen Hawking by combining quantum field theory in curved spacetime with the thermodynamics of black hole horizons. The derivation is internally consistent and several independent re-derivations (Unruh, Wald, Parikh-Wilczek) all converge on the same result. But for stellar-mass and larger holes, the predicted temperature is far below 1 K — for an 8,200 M☉ IMBH, T_H ≈ 7.5×10⁻¹² K, completely buried beneath the 2.7 K cosmic microwave background. Direct detection requires either a tiny BH that's about to evaporate (none discovered) or some way to thermally isolate from the CMB (no proposal works). Laboratory analog systems — sonic horizons in Bose-Einstein condensates (Steinhauer 2016) — have shown the predicted spectrum, but a curved-spacetime measurement remains open.
An IMBH-based civilisation would have a host whose Hawking lifetime exceeds proton decay by ~45 orders of magnitude. The MTH speculative scenario of compressing computation into a black-hole ergosphere therefore has effectively unlimited substrate lifetime relative to any other physical timescale — provided the surrounding universe isn't doing something interesting on cosmological timescales (heat death, vacuum decay, etc).
10⁹·⁷ yr: remaining solar lifetime before the Sun becomes a red giant.
10¹⁰·¹ yr: current age of the universe.
10¹⁴ yr: end of the stellar epoch — no more star formation, gas exhausted (Adams & Laughlin 1997).
10²⁰ yr: degenerate-stars era — white dwarfs cooling, occasional collisions.
10³⁴ yr: theoretical lower bound on the proton lifetime (Super-Kamiokande limit).
10⁶⁷ yr: solar-mass black hole Hawking lifetime.
10¹⁰⁰ yr: supermassive-BH Hawking lifetime.
Hawking's 1974 derivation (Nature 248:30) combined QFT in curved spacetime with thermodynamics. Several independent derivations since (Unruh 1976, Parikh–Wilczek 2000, Hartle–Hawking via Euclidean methods) all converge on the same spectrum. For curved-spacetime detection, the obstacle is temperature scale: a 1 M☉ hole has T_H = 6.2×10⁻⁸ K, ~8 decades below CMB. The first analog Hawking observation came from Steinhauer 2016 (Nature Physics 12:959) using a Bose-Einstein condensate sonic horizon — thermal spectrum confirmed, with refinements in 2019 and 2021. Other analog systems (water-wave horizons, optical-fiber analogs) have observed compatible signatures. The astrophysical observation remains open.
If a primordial BH formed in the early universe at ~1.7×10¹¹ kg, it would be evaporating today and producing a final-burst gamma-ray signature. Fermi-LAT (2008+) and ground-based atmospheric Cherenkov telescopes (HESS, MAGIC, VERITAS) have searched for these final-burst events with null results, placing a rate limit of ≲ 0.05 PBH bursts/pc³/yr (Albert et al. 2019). Across the full PBH mass range, dynamical microlensing (OGLE, Subaru HSC), CMB spectral distortions (FIRAS), and gravitational-wave (LIGO) constraints together rule out PBHs as the dominant dark matter component except in narrow mass windows (~10⁻¹⁶ to 10⁻¹⁰ M☉ asteroidal range and a small ~10–100 M☉ window).
The timeline strip ticks: age of universe 1.38×10¹⁰ yr (Planck 2018); solar lifetime remaining ~5×10⁹ yr to red giant onset (Sackmann, Boothroyd & Kraemer 1993); stellar epoch end ~10¹⁴ yr (gas exhaustion; Adams & Laughlin 1997); degenerate-stars era ~10²⁰ yr (cooling white dwarfs, occasional collisions); proton decay ~10³⁴ yr lower bound (Super-Kamiokande); solar-mass BH Hawking lifetime ~10⁶⁷ yr; supermassive Hawking lifetime ~10¹⁰⁰ yr (this is the famous "Black Hole Era" of cosmological epoch taxonomy). After ~10¹⁰⁰ yr the universe contains only photons and leptons — until the next something.