# What is the size of a black hole?

1. Apr 12, 2010

### Deepak Kapur

1. I repeat, 'what is the size of a black hole'.

2. Is there anything denser/smaller than a black hole?

2. Apr 12, 2010

### nicksauce

1. A black hole of mass M has radius R = 2GM/c^2

2. This question seems to assume that all black holes have the same size, which is false. At a given mass, a black hole would be the smallest, densest thing of that mass.

3. Apr 12, 2010

### jnorman

hmmm - from the wiki entry on this topic, they reference sean carroll:
"At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[38] For a non-rotating black hole this region takes the shape of a single point and for a rotating black hole it is smeared out to form a ring shape lying in the plane of rotation.[39] In both cases the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[40] The singular region can thus be thought of as having infinite density."

the NCSA website states:
"By definition a black hole is a region where matter collapses to infinite density..." implying zero volume.

the NASA website states:
"the center of a black hole spacetime has infinite curvature and matter is crushed to infinite density under the pull of infinite gravity. At a singularity, space and time cease to exist as we know them. The laws of physics as we know them break down at a singularity, so it's not really possible to envision something with infinite density and zero volume."

and:
"The star eventually collapses to the point of zero volume and infinite density, creating what is known as a " singularity ""

and penrose's paper (http://www.ias.ac.in/jarch/jaa/17/213-231.pdf) clearly states that a singularity (differentiating between singularity and schwarzchild radius) has infinite density, zero volume.

4. Apr 12, 2010

### nicksauce

All good points.

First we have to define what we mean by a black hole. Usually people define this to mean everything inside the event horizon, i.e., the ball 0 r < Rs, where Rs is the Schwarzschild radius.

Second, it is true that the density profile of the black hole will be zero everywhere except the singulariy (r=0) where the desntiy is infinite. However, it still seems sensible to talk about the average density of the black hole as M / (4/3 * pi * Rs^3).

5. Apr 12, 2010

### Medium9

I wonder if there could exist an object with non-zero volume (or non-infinite density) that has a schwarzschild radius. Something of the order of a quark star. Would that be possible?
And if so, would it be distinguishable from a BH formed by a singularity?

6. Apr 12, 2010

### silentbob14

2. A singularity at the moment of the big bang was smaller than any of the black hole singularities.

7. Apr 17, 2010

### Deepak Kapur

How is it possible when the volume is zero in either case?

8. Apr 17, 2010

### silentbob14

I think it's not zero, more like so close to zero that it's negligible. Though I'm not sure about this.

9. Apr 17, 2010

### silentbob14

10. Apr 17, 2010

### Nabeshin

All astrophysical black holes have some spin anyways, which means their singularities are actually rings.

Also, until anyone actually invents a viable theory of quantum gravity, I think we should hold off on speculating about what this theory might say about a singularity.

11. Apr 17, 2010

### silentbob14

This thread got me thinking. Shouldn't an object, which has a mass have a volume (bigger than zero)?

12. Apr 17, 2010

### S. Hardt

I found these 2 Quotes giving a good answer and I tried to explain it by looking for a similar problem.

If the density can still increase with the same mass, the Volume has to be more than zero but can approach it.

I would relate this "phenomena" with a heater that can heat water to 100 Celsius.
To get 100 Celsius a heater is needed that can add more energy than just for 100 Celsius.
If you look counter wise at the absolute 0 point,
you can never get colder, and that means you will never reach it exactly.
I think it is the same with the Volume of a black hole.

..but I am only a student interested in this so I hope it is all right

Last edited: Apr 17, 2010
13. Apr 17, 2010

### Medium9

I would actually relate it to the limit of some mathematical function that tends to zero. It'll never reach it, but get infinitely close. Something along the way of 1/x. That is, as long as there is room for speculation in this field, which I strongly hope will change within my lifetime!

14. Apr 18, 2010

### S. Hardt

If you want to write it as an equation you can write it as

Volume = Mass/Density

Volume the Space created by the energy of an atom(/particle?)

If it is possible to set up an equation with Density in relation to an energy used to form space for a single particle, you can rewrite this and get a really answer. The whole problem of this is that you can not easily determine this energy factor.
...but this goes into another sector.

I hope there is room for speculation...

15. Apr 18, 2010

### Nabeshin

I think you guys are mistakenly trying to apply a) common sense and b) simple mathematics/physics to a situation which is neither common nor simple.

For example, volume as measured by who? In relativity, different observers will see different volumes. Time as measured by who? Different observers measure different times... Just because intuition tells you something with mass must have nonzero size has no bearing on whether or not this is actually the case. Take an electron. No volume, yet a distinct mass, charge, spin.

From classical GR we know the following: Any matter inside the event horizon is doomed to fall inward and inward until it finally impacts the singularity. Therefore we conclude all matter is doomed to end up at a single point. As far as how long this takes for which observers, that's an incredibly trickier question. I can state, however, that for any particle falling through the event horizon, it will reach the singularity in a finite (and very short!) proper time. Of course, no one OUTSIDE the horizon could ever hope to observe any of this (and indeed, sees objects as taking an infinite amount of time to cross the horizon), so is it really of any consequence?

16. Apr 18, 2010

### S. Hardt

Thank you Nabeshin,
You are right it was the attempt to explain this phenomena by common sense and simple mathematics, and there is also no consequence.

I think I got some facts wrong and should study more before I contribute to a topic specific like this. Anyway I found another answer to one of my questions in what you wrote, and another somewhere in this Forum, too.

17. Apr 18, 2010

### AUK 1138

this is the size of the Schwarzschild radius, not the size of the black hole. by your definition, the black hole is a rather large object. when in reality, a black hole operates more like a point particle, ie a singularity.

18. Apr 18, 2010

### Frame Dragger

No, a singularity behaves that way, a Black Hole is the whole (PUN!) shebang: Event horizon, Ergoregion and singularity.

19. Apr 18, 2010

### ViewsofMars

Hello Deepak Kapur (OP), I think that The National Radio Astronomy Observatory should be of help to you in your search. It is a 'facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.' that means it's "A" ok!

20. Apr 19, 2010

### Frame Dragger

You do realize that has nothing to do with what he asked, or the course of the discussion? Nicksauce answered this question in the second post, which then led to