The simplest idealized black hole is the static isolated black hole. Real stars or black holes will rotate and not be static. Black holes in binary systems will not be isolated. Even if not very realistic, the idealized case does help us begin to understand the properties of static isolated black holes.
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Static Isolated Black Hole
Physicists often approach difficult problems by making idealized approximations to get a basic understanding. They then add complexities to gain a more realistic understanding of the real situation.
Event Horizon of a Static Isolated Black Hole
The boundary of the black hole is called the Schwarzschild radius or event horizon. At this boundary, the escape velocity equals the speed of light. From just outside the Schwarzschild radius, it is possible to escape the black hole by traveling outward at the speed of light.
From just inside, no escape is possible because the escape velocity exceeds the ultimate speed limit for the universe, the speed of light.
For a star the mass of the Sun, the Schwarzschild radius is about 3 kilometers. Its size is linearly proportional to the collapsed mass. A two solar mass black hole would have a Schwarzschild radius of 6 kilometers. A 10 solar mass black hole, 30 kilometers and so on.
Circumference Rather Than Radius
Astrophysicists specializing in black holes worry about a technicality. In normal flat space, the diameter and circumference of a circle or sphere have a simple and well known relation. The circumference is simply pi times the diameter.
However, near a black hole, space is so distorted that this simple relationship does not hold. Because the circumference of a static isolated black hole is farther from the center of this distortion, it is less distorted than the diameter or radius. Hence, black hole astrophysicists often prefer to talk about the circumference rather than the radius of a black hole.
Most people, however, are more familiar with the radius of a circle or sphere than the circumference. Hence, many ignore this technicality. References to the radius of a black hole refer to the radius it would have had space not been so distorted by the presence of the black hole.
Photon Sphere
Nothing can escape from the event horizon of a static isolated black hole. From just outside the event horizon, it is possible to escape by traveling at the speed of light, but escape is not automatic.
A space shuttle must be launched at an escape velocity to escape Earth’s gravity, but there is an additional requirement. It must be launched fairly close to straight up. Otherwise, the rocket will fall back to Earth, even if launched at its escape velocity.
Escaping from just outside the event horizon has a similar requirement.
A photon of light, which will of course be traveling at the speed of light, can escape from just outside the event horizon, but it must travel nearly straight outward. The directions are close enough to straight out that they allow the photon to escape from a cone called the exit cone.
Photons outside the event horizon that are moving outward outside the exit cone will fall back into the black hole even though they are traveling faster than the escape velocity. A photon pointed outward on the boundary of the exit cone will neither escape from nor fall back into the static isolated black hole.
It will simply orbit the black hole. This region outside the event horizon where the gravitational force is strong enough to allow photons to orbit the static isolated black hole is called the photon sphere.
Inside the Event Horizon of a Static Isolated Black Hole
Inside the event horizon, a static isolated black hole has a singularity point at the center, containing all the mass. The event horizon of a static isolated black hole, or Schwarzschild radius, surrounds the singularity and represents the boundary where the escape velocity equals the speed of light.
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Acceleration of a static observer near the event horizon of a static isolated black hole
