Black hole size comparisons

[Baby Astronaut]

Is there any?

 

What difference in 3D size exists between a tiny black hole and a super-massive one? For isn't a black hole simply a point with no dimensions regardless how massive?

 

If they do lack physical dimensions, and consequently have no size difference, is the radius of their event horizon the only difference in size?

[ajb]

Classically the singularity is a point, regardless of any other properties.

 

When one talks about the size of a black hole, one usually means the distance from the singularity to the event horizon. From the Schwartzchild metric we know this is

 

[math]r_{s} = \frac{G M}{c^{2}}[/math].

[iNow]

I tend to think of it as the BHs "sphere of influence." The event horizon is the distance from center whereby any object which passes that threshold cannot escape. It's the final point of gravity strong enough to prevent even light from escaping.

 

As ajb mentions, the singularity is a point, and that will be consistent regardless of the overall size/mass of the rest of the hole (actually, a singularity is a breakdown in our models/calculations more than anything else, but hey... go with it). What changes is the radius of the event horizon, the "Schwartzchild metric" ajb described.

 

As the hole feeds and takes in more matter/mass, it's event horizon grows... it increases its "sphere of influence." So, a tiny black hole may have a tiny event horizon, and hence won't really act on objects more than a rather small distance away. However, a supermassive blackhole may have a gigantic sphere of influence, spanning galaxies, and acts on objects across rather profound stellar distances. It's the Schwartzchild metric/radius that is being referred to when people discuss size of blackholes.

 

So... according to our current models, the singularity or center is the same regardless of BH size, but the extension of its gravity... its sphere of influence... is what will differ.

Edited August 7, 2009 by iNow

[ajb]

I tend to think of it as the BHs "sphere of influence."

 

A technical problem with thinking like that is that gravity is a long-range force. In classical general relativity this manifests itself as a question of "asymptomatic flatness ", that is far enough away from the object the gravity is negligible. The Schwarzschild metric has this property, but not all vacuum solutions do.

 

So, in this sense an isolated black hole is infinite in size!

[Sisyphus]

I think of it as more significant than just a sphere of influence. No information can escape from "inside," so from a positivist perspective "inside" doesn't even exist, just the "hole" of a given radius. Any path from a point inside just leads elsewhere inside, so it's sort of its own little semi-universe.

[iNow]

Indeed. You are both, of course, correct. A poor choice of words on my part. Since gravity is a long range force it will just redshift more and more as distance increases, but never really cease its influence all the way. I intended to refer specifically to the "total area surrounding the blackhole whereby the gravity is so strong that not even light can escape." The size of that area is what people mean when they refer to the size of the blackhole.

[Airbrush]

...However, a supermassive blackhole may have a gigantic sphere of influence, spanning galaxies....

 

Not spanning galaxies. Even the most massive black hole known, OJ287 at 18 Billion Solar, has an accretion disk only a little larger than our solar system, about 1/5 of a light year (extending out to about the middle of the inner Oort Cloud), and superimposed over our solar system it has an event horizon extending only to within the orbit of Mercury. More correct to say "spanning interstellar space".

 

http://stardate.org/resources/news/blackholes/200801a.html

 

My favorite bit of trivia: If the Earth was crushed down into a black hole the event horizon would form a sphere less than one inch in diameter! It would look like a small flat-black super ball.

Edited August 11, 2009 by Airbrush