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This chapter describes Hawking's groundbreaking discovery that black holes emit radiation. In November 1970, Hawking realized that the area of a black hole's event horizon can never decrease - it must stay constant or increase when matter falls in or when black holes merge. This behavior remarkably resembles entropy in thermodynamics, which also never decreases according to the second law. Jacob Bekenstein suggested the area represents the black hole's entropy, but this implied black holes should have temperature and emit radiation, contradicting their definition. In 1972, Hawking, Carter, and Bardeen wrote a paper noting the similarities but rejecting the entropy interpretation. However, in 1973 after discussions with Soviet physicists Yakov Zeldovich and Alexander Starobinsky, Hawking calculated that quantum mechanical effects cause black holes to emit particles. The mechanism involves virtual particle-antiparticle pairs that constantly appear in empty space due to the uncertainty principle. Near a black hole's event horizon, one particle with negative energy can fall in while its partner escapes as real radiation. This makes the black hole appear to glow with a temperature inversely proportional to its mass - smaller black holes are hotter. As black holes radiate, they lose mass and eventually evaporate completely in a final explosion. Stellar-mass black holes have extremely low temperatures and would take 10^66 years to evaporate, but primordial black holes with masses around a billion tons would be completing their evaporation now, emitting gamma rays. Though searches have not found them, the gamma ray background limits their abundance to about 300 per cubic light-year. The discovery of Hawking radiation was initially met with skepticism but became accepted as a crucial result combining general relativity and quantum mechanics. It suggests gravitational collapse may not be completely irreversible, and hints that quantum mechanics might eliminate singularities.