HAWKING TEMPERATURE

Black holes as thermal blackbodies radiating at T = ℏc³/(8πGMk_B)

10 M☉
0%
2.0
Hawking radiation (1974) showed that quantum effects cause black holes to emit thermal radiation with temperature T = ℏc³/(8πGMk_B). For a solar-mass black hole this is an astonishing 6×10⁻⁸ K — far below the CMB. As the hole radiates it loses mass, which raises T, which increases emission rate, ending in a runaway evaporation. A black hole of mass M evaporates in time τ ∝ M³. Primordial black holes with mass ~10¹² kg would be evaporating right now, producing a burst of gamma rays. The spectrum is exactly that of a blackbody, encoding deep connections between gravity, quantum mechanics, and thermodynamics.