Hawking’s black hole area theorem says the total area of an event horizon can never decrease.
In classical general relativity, the event horizon is the boundary beyond which light cannot escape to the outside universe. Hawking’s theorem states that, provided the usual weak energy condition holds, the horizon’s area is non-decreasing over time. When black holes merge, for example, the final horizon area must be at least as large as the sum of the original areas.
The result became known as the second law of black-hole mechanics because it resembles the second law of thermodynamics: entropy does not decrease. Jacob Bekenstein proposed that black-hole entropy should be proportional to horizon area, and Hawking’s later quantum calculation established the Bekenstein–Hawking relation, S = kA/(4ℓₚ²).
The other options are different structures. An accretion disk is hot material orbiting outside the hole, an ergosphere surrounds a rotating black hole outside its horizon, and a photon sphere is a region where light can orbit. None is the boundary governed by Hawking’s area theorem.