What defines the event horizon of a black hole?
The event horizon of a black hole is defined by its Schwarzschild radius.
The Schwarzschild solution of Einstein's Field Equations is valid for a vacuum surrounding an uncharged, non rotating massive body. The Schwarzschild solution has two singularities at radii
The first singularity is at
The second singularity defines the Schwarzschild radius
For most bodies the Schwarzschild radius is much smaller than the radius of the body which invalidates it. If all of the mass of a body is compressed to a volume smaller than the Schwarzschild radius
the equation becomes truly singular at
If a body is smaller than its Schwarzschild radius it has what is called an event horizon at
At the event horizon, gravitational time dilation makes time stop. This also means that the escape velocity is the speed of light. This effectively describes a black hole from which nothing, not even light, can escape.
Although the theory predicts black holes, few people believed that they existed until 1964 when a strong radio source called Cygnus X-1 was discovered. It was soon universally accepted that Cygnus X-1 had to be a black hole.