# What defines the event horizon of a black hole?

May 6, 2018

The event horizon of a black hole is defined by its Schwarzschild radius.

#### Explanation:

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 $r$ where one of the terms becomes infinite.

The first singularity is at $r = 0$. As this is inside the body, it falls outside of the constraints of the solution.

The second singularity defines the Schwarzschild radius ${r}_{s}$.

${r}_{s} = \setminus \frac{2 G M}{{c}^{2}}$

Where $G$ is the gravitational constant, $M$ is the mass of the body and $c$ is the speed of light.

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 $r = {r}_{s}$.

If a body is smaller than its Schwarzschild radius it has what is called an event horizon at $r = {r}_{s}$.
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.