A boundary of a black hole that depends on the observer and responds to changes in mass, unlike the event horizon.An apparent horizon is a boundary in a black hole spacetime that is defined locally, based on the behavior of outgoing light rays at a given moment. Unlike the event horizon, which is a global concept requiring knowledge of the entire future of the universe, the apparent horizon depends on the observer's choice of time slicing and can change in response to matter falling into the black hole. It is the outermost surface where all outgoing light rays are converging, meaning even light cannot escape outward.
The concept was introduced by Roger Penrose in 1965 as part of his work on gravitational collapse and singularity theorems. It was later refined by Stephen Hawking and George Ellis in their 1973 book 'The Large Scale Structure of Space-Time'.
The apparent horizon is defined using the concept of trapped surfaces: a surface where both ingoing and outgoing light rays are moving inward. The apparent horizon is the boundary of the region containing trapped surfaces. It can be computed from the local geometry of spacetime at a given time, making it useful for numerical simulations of black hole mergers, where the event horizon is difficult to track in real time.
Apparent horizons are routinely used in numerical relativity to locate black holes in simulations of mergers and to compute their masses and spins, as they can be found from the instantaneous data of the simulation.
In a dynamic black hole merger, the apparent horizon can appear and grow before the event horizon forms, and it is always located inside the event horizon, never outside.















