What defines the event horizon of a black hole?

Answer 1

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.

Black holes are predicted by the theory, but until the discovery of a powerful radio source known as Cygnus X-1 in 1964, few people thought that black holes actually existed. After that, it was widely accepted that Cygnus X-1 must be a black hole.

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Answer 2

Emma Arguello

The point beyond which nothing can escape a black hole's gravitational pull—not even light—is known as the event horizon.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.