What theorem states that a black hole's event horizon area never decreases?

The theorem stating that a black hole’s event-horizon area never decreases is the black hole area theorem, also called Hawking’s area theorem.

In classical general relativity, the theorem says that the total area of black-hole event horizons cannot decrease with time, provided suitable energy conditions hold. During a merger, for example, energy can escape as gravitational waves and the final black hole can spin differently, yet the final horizon area must be at least as large as the combined initial areas.

Roger Penrose and Stephen Hawking developed the mathematical foundations of the result in the early 1970s. Its resemblance to the second law of thermodynamics helped inspire the idea that horizon area behaves like entropy. Jacob Bekenstein proposed this connection in 1972, and Hawking’s later work established that black holes possess a temperature through quantum effects.

The area theorem is not identical to the generalized second law of thermodynamics. Hawking’s theorem is a classical result and can be modified by quantum effects such as Hawking radiation. The generalized law instead tracks the combined entropy of the black hole and its surroundings.