The Core

How big is a black hole?

The size of a black hole is the size of the Schwarzschild radius. It is also called the event horizon. Once something is within this radius, it's gone; it will inevitably fall into the singularity at the center of the black hole. The derivation of the Schwarzschild radius is quite simple. But if you don't want to do it, you may jump it here.

The Schwarzschild radius is where even the kinetic energy of a photon is not sufficient to escape from the black hole. The kinetic energy is given by the formula:

,

From a classical point of view we can assume that a photon is radiated from the singularity at the center of a black hole at the speed of light and while it reaches a greater and greater distance, it's kinetic energy is slowly turned into potential energy. Nothing can get past the radius where the potential energy of a photon is as great as its kinetic energy was at the time it was emitted from the singularity.

The potential energy a particle has at a distance R of a black hole is given by Newton's formula:

.

It is also important to mention that the speed of light in vacuum is constant. You probably know this already. This means that a photon can't be slowed down even if it loses its energy. Is this a contradiction? No! A photon isn't slowed down, but its color shifts to the less energetic red and therefore also loses kinetic energy. Thus we can equate the two energy formulas from above:

m: mass of the photons radiated from the singularity
c: speed of light;
G: gravitational constant;
M: mass of the black hole
R: Schwarzschild radius

That was easy. Now we know how big the Schwarzschild radius is. Even though this is only a classical derivation it's result is the exact formula.

Let's do some calculations !

What size would a black hole with the mass of the Earth have?

The mass of the earth is about .

The Earth Image Number: AC75-0027 Photographer: Apollo 16 Date: April 16, 1972 Courtesy of NASA Ames Imaging Library Server

A black hole with the mass of the Earth would be less than two centimeters (just 0.7 inches) across!!

Remember the story "The Hole Man" we introduced?

First Photo From Mars Image Number: AC76-1011-1-46 Photographer: Viking 1 Date: July 21, 1976 Courtesy of NASA Ames Imaging Library Server

The black hole in "The Hole Man" has a mass of . That's already the mass of a mountain. Well, how big (or small) would this black hole be? Another calculation:

This is much smaller than an atom!

"Black holes aren't black - After Hawking they shine!"
Presented by Angie, Matthias and Thorsten
Team C007571,ThinkQuest Internet Challenge 2000.
Last modified: 2000-08-02.