Event Horizon and Photon Sphere

Static Isolated Black Hole Structure Outside Schwarzschild Radius

Aug 26, 2007

A static isolated black hole has an event horizon or Schwarzschild radius surrounded by a photon sphere.

Static Isolated Black Hole

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 in addition not be isolated. Even if not very realistic, the idealized case does help us begin to understand the properties of black holes.

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 or Schwarzschild Radius

The boundary of the black hole is called the Schwarzschild radius or event horizon. On 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 well known relation. The circumference is simply pi times the diameter.

Near a black hole however space is so distorted that this simple relationship does not hold. Because the circumference of a 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 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 were space not so distorted by the presence of the black hole.

Photon Sphere

Nothing can escape from inside the event horizon. 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 the 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 the 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 close enough to straight out that allow the photon to escape form 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 black hole. It will orbit the black hole. This region outside the event horizon where the gravitational force is strong enough to allow photons to orbit the black hole is called the photon sphere.

Inside the Event Horizon

Inside the event horizon, a static isolated black hole has a singularity point at the center containing all the mass. The event horizon or Schwarzschild radius surrounds the singularity and represents the boundary where the escape velocity equals the speed of light.