The video explains that an event horizon is not simply the visible “black disc” of a black hole. Formally, it is the boundary of the causal past of future null infinity – the set of events that can still send light out to infinite distance. Because this definition depends on the entire future of spacetime, the horizon can exist and even expand before any matter has actually collapsed; a light‑trapped surface may already be forming around you without you knowing it.
In dynamical situations (e.g., collapsing shells or merging black holes) physicists also use the *apparent horizon*: the locally outermost surface from which outward‑directed light rays make no progress. The apparent horizon is frame‑dependent and can change with the slicing of spacetime, but it always lies inside or on the true (teleological) event horizon. While the apparent horizon is useful for simulations and for describing the instantaneous, observable edge of a black hole, the true event horizon remains a global, future‑dependent boundary that defines what can ultimately escape to infinity. Thus, distinguishing between the two concepts resolves ambiguities about where and when a black hole’s horizon actually exists.
1. The event horizon is defined as the boundary from which light cannot escape.
2. To be considered outside the event horizon, light must be able to reach infinite distance (future null infinity).
3. The formal definition states that an event horizon is the boundary of the causal past of future null infinity.
4. In a Penrose diagram, future null infinity is where light rays end in the infinite future.
5. For an eternal black hole, one future null infinity is replaced by the event horizon on the diagram.
6. Inside the event horizon, space and time grid lines interchange; moving upward corresponds to falling deeper toward the singularity.
7. Nothing can escape because escaping would require a trajectory shallower than 45°, i.e., faster than light.
8. The event horizon is non‑local; it depends on the entire spacetime and future events, not just a local point.
9. Physicists sometimes describe the event horizon as teleological, relating to the final state of the universe.
10. An event horizon may have already passed a location without any local indication of its presence.
11. In the Vaidya (collapsing radiation) spacetime model, the event horizon forms before the black hole and grows outward at the speed of light.
12. The apparent horizon is the locally inescapable boundary, defined as the outermost surface from which outward‑directed null geodesics converge.
13. The apparent horizon lies inside or on the true event horizon for any spacetime.
14. Unlike the true event horizon, the apparent horizon varies with the observer’s frame of reference and slicing of spacetime.
15. In simulations of merging black holes, the apparent horizon of each inspiraling hole warps as they approach.
16. A joint apparent horizon of the merged black hole forms only at the instant the true event horizons merge.
17. The true event horizon is a causal boundary extending through spacetime, not merely a local surface.
18. The apparent horizon provides a useful, conservative estimate of a black hole’s extent for studying dynamical systems such as quasars or mergers.
19. The singularity inside a black hole occupies all future times within the event horizon.
20. Light that starts exactly at the event horizon remains trapped there forever and inevitably reaches the singularity.