T_H = ℏc³/(8πGMk_B), virtual pair creation, evaporation timeline, information paradox
T_H = ℏc³/(8πGMk_B) ≈ 6.17×10⁻⁸ K · (M☉/M)
Evaporation time: τ ≈ 5120πG²M³/(ℏc⁴) ≈ 8.41×10⁻¹⁷ s · (M/kg)³
Hawking (1974): quantum field theory in curved spacetime → black holes emit thermal radiation. Near-horizon, virtual particle pairs from vacuum fluctuations split: one falls in (negative energy), one escapes → BH loses mass. Spectrum is exactly Planckian at T_H. Evaporation time ∝ M³ — a solar-mass BH takes 10⁶⁴ yr; Planck-mass BH evaporates in ~10⁻⁴³ s. Information paradox: unitary QM vs thermal radiation — Page (1993) curve, islands formula (2019). Kerr BH: superradiance modifies spectrum; T_H=0 at a=M (extremal).