Size of black hole

I am wondering about size of black hole. How is it possible that we have black holes of different sizes? As I know the singularity is point which is infinite small and is infinite dense. So my question is how can infinite dense and infinite small object create different size black holes. We have different big infinite singularities?

• Usually when we talk about the size of the black hole we're talking about its event horizon. You're right it doesn't make much sense to talk about the size of the singularity. Plus, due to the extremely distorted space I'm pretty sure you can measure an arbitrarily long length inside of the black hole that's arbitrarily small outside of it. That is, I'm pretty sure the curvature allows a black hole to be "much bigger" inside than it is outside. – Brandon Enright Aug 3 '14 at 22:23
• @BrandonEnright: I think you might want to make that a separate question and spell out in more detail what you have in mind. – Ben Crowell Aug 3 '14 at 23:02

A black hole has two main features:

1. a singularity
2. an event horizon

The event horizon is a sphere with a certain radius. Most people visualize the singularity as a point at the center of the sphere, and although that's not quite rigorously right, it's good enough for the purposes of the present discussion.

Using a rough Newtonian analogy, the event horizon is like the surface from which the escape velocity exceeds the speed of light. In the real relativistic theory, it's boundary that no cause-and-effect relationships can cross from the inside out.

Black holes form by the gravitational collapse of massive bodies. You can think of the singularity as the place where all the in-falling matter accumulated.

When people talk about the radius of a black hole, they usually mean the radius of the event horizon.

Thank you, but what is making that diference between sizes of event horizons (we have got super massive black holes, smaller blackholes? I mean how is possible that one blackhole is smaller than the other or bigger when singularity is just infinite in size and mass ?

Different black holes have singularities containing different amounts of mass. The mass is not infinite. For example, if a star with a mass of 6 solar masses collapses to form a black hole, then the black hole is a 6-solar-mass black hole. The size of the event horizon is proportional to the mass.

• Thank you, but what is making that diference between sizes of event horizons (we have got super massive black holes, smaller blackholes? I mean how is possible that one blackhole is smaller than the other or bigger when singularity is just infinite in size and mass ? When is once something infinite small and infinite dense why it doesn´t create still same big black hole ? why is that event horizon still different in size ? Or singularity is that point in the middle and around him there is another mass which is creating size of black hole ? Sorry for english. – Tomas Klema Aug 3 '14 at 22:26
• Hi Ben, welcome back :-) I made a comment above on the question suggesting the curvature inside of the black hole does strange things with "length". Am I completely off? Can you say more about what reference frame the radius is measured in? – Brandon Enright Aug 3 '14 at 22:26
• @TomasKlema: I edited the answer to respond to your comment. – Ben Crowell Aug 3 '14 at 23:00

Different black holes have different masses. For non-rotating black holes, the distance $$r=\frac{2Gm}{c^2}$$ describes the event horizon. As you can see, the mass $m$ of the black hole enters here. This WP page on the Schwarzschild radius describes has more information.

So my question is how can infinite dense and infinite small object create different size black holes.

The singularity within a black hole is not the crucial consideration here.

If an amount of (non-spinning, non-charged) mass $M$ is contained within a volume of radius of $r_s = \frac{2GM}{c^2}$, the mass $M$ is 'hidden' within a spherical event horizon (black hole) of radius $r_s$.

Thus, the larger the mass $M$, the larger the radius $r_s$ of the black hole.

The result that the mass cannot remain static within the horizon and must collapse to a singularity is secondary to the above result.