The surface area of a black hole's event horizon, related to its entropy.Horizon area is the surface area of a black hole's event horizon, the boundary beyond which nothing can escape. In classical general relativity, the horizon area is a crucial quantity: it never decreases (the second law of black hole mechanics) and is directly proportional to the black hole's entropy, as shown by Bekenstein and Hawking. This connection between geometry and thermodynamics is a cornerstone of our understanding of quantum gravity.
The area theorem was proven by Stephen Hawking in 1971, and the entropy connection was proposed by Jacob Bekenstein in 1972, with Hawking's subsequent work on black hole radiation solidifying the relationship.
The event horizon is a null surface defined by the escape velocity equaling the speed of light. Its area is computed from the spacetime metric, typically using the Kerr-Newman solution for rotating, charged black holes. The area increases when matter or energy falls into the black hole, and it is related to entropy via the Bekenstein-Hawking formula: S = A/(4ℓ_Pl²), where ℓ_Pl is the Planck length.
Horizon area is used in gravitational wave astronomy to infer the properties of merging black holes, and in theoretical models of black hole thermodynamics and information paradox resolution.
If you throw a book into a black hole, the increase in horizon area is proportional to the entropy of the book's information, a fact that inspired the holographic principle.














