What defines the event horizon of a black hole?

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May 6, 2018


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 #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 = \frac{2GM}{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.

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