# How big is a BLACK HOLE? Can it be calculated ?

1. Jan 25, 2004

### timejim

How big is a BLACK HOLE? Can it be "calculated"?

I was curious as to whether or not the size of a Black Hole can be calculated. If known, can the size of black holes vary, I mean, are there small ones, large ones, etc.?

2. Jan 25, 2004

### mathman

The size of a black hole is defined by its mass. For a given mass, there is a length called the Schwarzschild radius, which is proportional to the mass. If the object in question is small enough to be inside this radius, it is a black hole. Anything crossing this boundary then becomes part of the black hole.

3. Jan 25, 2004

Staff Emeritus
So the answer to the question is, they can be any size, but for a given size, the mass is huge. A black hole the size of a smll seed would have the mass of a mountain range (or so I am told by Charles Stross' sf novel Singularity Sky, and I have every reason to believe he did his homework) :=).

4. Jan 25, 2004

### meteor

In general relativity, the most factible type of black hole is a Kerr black hole, that have a singularity with the shape of a ring.They have two, not one, event horizons
It has been proposed to create artificial little black holes here in laboratories in earth. These are called optical black holes

5. Jan 26, 2004

### marcus

Re: How big is a BLACK HOLE? Can it be "calculated"?

the size of a black holes varies all over the place

a black hole with the mass of the sun would have a 6 kilometer diameter

a black hole with the mass of the planet jupiter would have a five to six meter diameter, I forget exactly

it is easy to calculate the radius if you know the mass, especially in the fairly ordinary case where you assume the hole is not electrically charged and not rotating. then it is an ordinary "
schwarzschild" which is to say "kosher" black hole and there is a real simple formula for the radius of the spherical event horizon which light doesnt escape from and which you must not touch

the size of the event horizon is what people ususally mean by the size of the hole

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Say M is the mass of the stuff that collapsed to make the hole, the mass of the hole itself in fact

And G is the famous Newton constant 6.674 E-11 cubic meter per sq. second per kilogram.

the radius of the event horizon (the dark ball that it is good to stay away from)
is 2GM divided by the square of the speed of light

$$\frac{2GM}{c^2}$$

So take an example! Suppose M is 9 E27 kilograms

Then multiply by G and you get 6.674x9 E16 cubic meter per sq second.

And divide by square of speed of light which is 9 E 16 sq. m per sq. second

You get 6.674 meters so twice that is the radius of the hole

the hole is around 13 meters radius or 27 meters diameter.

Well you asked about calculating the size of the thing. It is not my fault if it comes out a bit dumb and clunky. Calculation has that aspect.

Last edited: Jan 26, 2004
6. Jan 26, 2004

### Jeebus

Re: How big is a BLACK HOLE? Can it be "calculated"?

In principle there really is no limit on how big a black hole can get or have. Any amount of mass at all can in principle be made to form a black hole if you compress it to a high enough density. Logically though, however big the black hole is you can assume that is how big the massive star was. Also Astronomers suspect that many galaxies harbor extremely massive black holes at their centers, and some of these black holes are million times the more mass of our Sun, or or 10^{36} kilograms.

Ted Bunn: