Understanding the Event Horizon

1. The Event Horizon as a Global Concept

The event horizon is not a physical surface but a mathematical boundary beyond which nothing can escape. Its location depends on all future events in spacetime.

Why is it global?

  • The event horizon is defined by whether any signal sent from a point in spacetime can reach a distant observer.
  • Since we need to track light paths indefinitely into the future, the event horizon’s position is determined only by considering the entire spacetime evolution.

Light Cones and the Horizon

Light cones show the possible future paths of light. Near a black hole:

  • Far from the black hole: light cones are open, allowing escape.
  • At the event horizon: the cone tips inward, making escape impossible.
  • Inside the event horizon: light cones point entirely toward the singularity.
      Far from the black hole:
          Future light cones open outward
                 |    
                 v    
        \       |       /
         \      |      /
          \     |     /
------------------------------
      Event Horizon (null boundary)
          \     |     /
           \    |    /
            \   |   /
Inside BH:  \  |  /  (light cannot escape)
             \ | /
              \|/
          Singularity

2. The Event Horizon as a Family of Null Geodesics

Null geodesics are paths that light follows through spacetime. The event horizon consists of a family of light rays that just barely fail to escape.

Key Features:

  • Outside the horizon, light can escape.
  • On the horizon, light is “trapped,” neither falling in immediately nor escaping.
  • Inside the horizon, even light is forced toward the singularity.

3. Formation of the Event Horizon

During gravitational collapse, an event horizon forms before the singularity appears. Initially, some light may escape, but once inside the horizon, escape is impossible.

    Stage 1: Star collapsing, some light escapes
       *********    
      *         *    
     *    ⨀    *   --> Some light escapes
      *         *    
       *********

    Stage 2: Event horizon forms
       *********
      *    ●    *   --> Light at horizon is "trapped"
      *         *
       *********

    Stage 3: Black hole fully formed, no escape
       *********
      *         *   --> All paths lead to singularity
      *   ▽     *
       *********

4. Interactive Simulation

For a dynamic visualization of how light behaves near an event horizon, explore the interactive simulation below:

Inside a Black Hole – Interactive Simulation

5. Conclusion

  • The event horizon is a global concept: You need to consider all future light paths to define it.
  • It consists of null geodesics: Light rays that never escape but also never instantly fall into the singularity.
  • It evolves dynamically: The horizon forms before the singularity and expands as mass increases.