Hawking radiation

Hawking radiation is the thermal emission predicted to stream outward from the event horizon of a black hole. Discovered by Stephen Hawking in 1974, it arises when quantum fields are evolved through the curved, time-dependent spacetime of a collapsing star: an observer far away no longer sees the quantum vacuum but instead a steady blackbody flux of particles. The spectrum is exactly Planckian at the Hawking temperature T_H = ℏc³/(8πGMk_B), which is inversely proportional to the black hole's mass — large holes are extraordinarily cold, small holes are hot.

Because the hole radiates, it loses energy and therefore mass. Treating the horizon as a blackbody of area A = 16πG²M²/c⁴ at temperature T_H and applying the Stefan–Boltzmann law gives a luminosity L ∝ 1/M²: the smaller the hole, the more fiercely it shines. The mass loss is consequently a runaway, and the total evaporation lifetime scales as the cube of the mass, τ ∝ M³, ending in a final burst of high-energy radiation once the hole approaches the Planck mass and known physics breaks down.

Hawking radiation has never been observed from an astrophysical black hole and likely never will be: every real black hole is far colder than the 2.725 K cosmic microwave background and so absorbs more than it emits, net-growing rather than evaporating. Its significance is theoretical. It established that black holes are genuine thermodynamic objects with temperature and entropy, tied a horizon's surface gravity to a temperature, and created the black-hole information paradox — the still-unresolved conflict between the apparent loss of information in thermal evaporation and the reversibility demanded by quantum mechanics. The formula remains the single sharpest clue to a future theory of quantum gravity.

Jacob Bekenstein proposed in 1972–73 that black-hole entropy is proportional to horizon area; Hawking, attempting to disprove the implied temperature, instead derived the radiation in early 1974 and published 'Black hole explosions?' in Nature in March 1974, with the full derivation in Communications in Mathematical Physics in 1975.