Which theorem states that the total area of a black hole’s event horizon cannot decrease?

The black hole area theorem states that the total area of a black hole’s event horizon cannot decrease in classical general relativity.

Stephen Hawking proved the theorem in 1971 using the mathematical properties of event horizons and the requirement that matter obey ordinary energy conditions. In a merger, the separate horizons become one, and the final horizon’s area is at least as large as the combined initial areas.

The result resembles the second law of thermodynamics, whose entropy also does not decrease in an isolated system. This resemblance helped inspire black-hole thermodynamics, in which horizon area is proportional to entropy.

The theorem is classical: it does not include quantum effects. Hawking radiation can slowly reduce a black hole’s mass and horizon area, so the generalized second law combines black-hole entropy with the entropy of matter and radiation outside the hole.