# Density of black holes?

1. Jun 1, 2004

### taylordnz

if a black hole has infinte density wouldnt that mean it has infinite mass because its equation is

volume x mass = density

2. Jun 1, 2004

### mathman

That's a big if. In fact, the mass is finite. How it's distributed inside is an open question. Quantum theory and general relativity are in conflict.

3. Jun 2, 2004

### jcsd

You've got the equation wrong: it's mass/volume = desnity

The mass of a black hole is finite, it reason why a black hole has infinite density is that it's mass is concentrated into a space of zero-volume. It may be that the singularity is avoided, but this is highly speculative.

4. Jun 8, 2004

### techwonder

There's a lot of talk about the singularity in black holes. In general though, a theory coming up with infinities basically hints us that something is wrong. Or in other words - singularities do not exist.

5. Jun 22, 2004

### ArmoSkater87

To make it quick and easy, black holes definitly have finite mass. Before the black hole is formed it is a super massive star...which has finite mass and therefore finite density. So when it collapses, according to common sense it must still have finite density, but its just like jcsd said though, because mathematically the density becomes infinite since you would be dividing by zero volume.

Last edited: Jun 22, 2004
6. Jun 22, 2004

### ArmoSkater87

heh, but im having a hard time conprehending how something with a volume can be crushed into no volume.

7. Jun 22, 2004

### Integral

Staff Emeritus
We have no concrete knowledge of what happens inside the event horizon of a black hole. Any comments on the physical dimensions of the mass inside the event horizon are pure speculation. We can only know the total mass from exterior measurements not the configuration of the mass, only that it is contained within the radius of the event horizon.

8. Jun 22, 2004

### ArmoSkater87

yep...true true

9. Jun 23, 2004

### jcsd

Ah yes, but the Scwarzchild solution can be extended into the event horizon right up to the singularity, so if we assume general relatvity is correct we have a resoanble idea what's going on in there.

10. Jun 23, 2004

### Labguy

No so. The only thing we can say today is exactly what Integral posted. There is no solution in either GR or QM that we can be certain of that yet "stands the test".

11. Jun 23, 2004

### jcsd

Yu can be certain that GRvstands the except when microscale physics become important. The problem is if you reject GR then there's not much point in talking about black holes anyway. It is reasonable to assume that GR holds within certain parameters.

12. Jun 23, 2004

### Integral

Staff Emeritus
I am sure that GR can be extended beyond the event horizon in a meaningful fashion. But we know that somewhere inside there Physics as we know it breaks down (The singularity) the question we cannot answer is WHERE the breakdown occurs. Thus I say, that any comments concerning the state of matter inside the event horizon are speculative.

13. Jun 24, 2004

### Orion1

Schwarzchild Scheme...

The BH density is determined from its photon sphere and its event horizon and quantum singularity.

Although there is a radial Schwarzchild Solution in classical GR, BH density cannot be determined from this radial solution, because non-rotating event horizons do not exist.

The mass of a Chandresekhar BH is:
$$M_c = 1.457 M_o$$

The radial solution for a spherically symmetric Chandresekhar BH photon sphere is:
$$r_c = \sqrt[3]{ \frac{3 M_c}{4 \pi \rho_c}}$$

The radial solution for a spherically symmetric rotating gravitational BH event horizon is:
$$r_g = \frac{G M_c}{c^2}$$

$$r_c = r_g$$

$$\sqrt[3]{ \frac{3 M_c}{4 \pi \rho_c}} = \frac{G M_c}{c^2}$$

Density solution for spherically symmetric rotational gravitational Chandresekhar BH:
$$\rho_c = \left( \frac{3c^6}{4 \pi G^3 M_c^2} \right)$$

This density formula does not violate QM or GR and exists at QM and GR 'quantum shutdown'.

For densities at $$r_c < r_g$$ a formula must be demonstrated that does not violate QM or GR.

College Physics 101 - Entrance Examination:

Based upon the Orion1 Equations:

What is the mass of a Chandresekhar BH?

What is the radius of a Chandresekhar BH photosphere?

What is the density of a Chandresekhar BH?

Sorry, but you failed to qualify for this course.

Last edited: Jul 1, 2004
14. Jun 24, 2004

### Labguy

The "test" to which I was referring is at the "microscale" you mention. There is no way I would reject GR. In fact, I have all my money on the bet that all the "other experiments" about to be conducted (LIGO, etc.) will all confirm GR to the point where any doubters will have to concede. Since 1919 there have been too many confirmations on so many areas (predictions) of GR that I don't believe it is possible for it to fail, in as far as it went.

15. Jun 24, 2004

### jcsd

I think you're slightly confusing applications of the Scwarzchild solution. The Chandrasekhar limit is the maximum mass of a white dwarf and it comes from the degenracy pressure between electrons and nucleons, above this mass a white dwarf will become a neutron star (which has it's own limit).

The Scwarzchild solution can be used to describe the space around any spherically symmetric mass, which includes white dwarfs and neutron stars; classical black holes don't have photospheres, though they do have photon spheres.

16. Jun 25, 2004

### Orion1

Schwarzschild Scheme...

I think you're slightly confusing applications of the Scwarzchild solution. The Chandrasekhar limit is the maximum mass of a white dwarf and it comes from the degenracy pressure between electrons and nucleons, above this mass a white dwarf will become a neutron star (which has it's own limit).

jcsd, what you have said is correct, and your confusion is understandable, by 'Chandrasekhar BH', I am referring to the Chandrasekhar Mass Value as applied to a BH, not the mass limit of a White Dwarf, although this may also be introduced as a comparative point.

However, since this topic has been introduced, what is the radius and density of a Chandrasekhar neutron star with a Chandrasekhar Mass?

Now for comparative purposes of density realization, compare these values to the Chandrasekhar BH radius and density demonstrated above?

Anyone, please post the values that you have calculated.

The Scwarzchild solution can be used to describe the space around any spherically symmetric mass, which includes white dwarfs and neutron stars; classical black holes don't have photospheres, though they do have photon spheres.

The Schwarzschild Solution is a solution in Classical GR that describes the event horizon around a spherically symmetric 'non-rotating' BH.

Applying the Schwarzschild Solution to objects with high spin is a poor description of the space-time around 'high spin' objects such as white dwarfs, neutron stars, however can be used to describe the space-time around 'non-rotating' classical BHs, which do not exist anyway.

The mass of a Chandresekhar BH is:
$$M_c = 1.457 M_o$$

The radial solution for a spherically symmetric Chandresekhar BH sphere horizon is:
$$r_c = \sqrt[3]{ \frac{3 M_c}{4 \pi \rho_s}}$$

The radial Schwarzschild Solution for a spherically symmetric gravitational BH event horizon is:
$$r_s = \frac{2 G M_c}{c^2}$$

QM/classical GR shutdown:
$$r_c = r_s$$

$$\sqrt[3]{ \frac{3 M_c}{4 \pi \rho_s}} = \frac{2 G M_c}{c^2}$$

Schwarzschild Density Solution for spherically symmetric gravitational Chandresekhar BH:
$$\rho_s = \left( \frac{3c^6}{32 \pi G^3 M_c^2} \right)$$

Based upon the Orion1 Equasions:

What are the radius and density values of a Chandrasekhar neutron star with a Chandrasekhar Mass?

What are the radius and density values of a Chandrasekhar BH with a Chandrasekhar Mass?

What are the classical Schwarzschild radius and density values for a Schwarzschild-Chandresekhar BH?

Last edited: Jul 1, 2004
17. Jun 25, 2004

### jcsd

Orion1, the value you've posted in the Chandrasekhar limit and it applies to white dwarves, It comes from electron degenracy, not neutron degenrancy. The Chandrasekhar limit is the maximum possible mass of a white dwarf, any white dwarf with a mass greater than this will collapse into a neutron star, not a black hole.

The value that is comparitve to the Chandrasekhar limit for a neutron star is about 4 solar masses, though realistically a neutron star cannot have a mass greater than 2 solar masses.

A black hole of a mass of about 1.4 solar masses could not realtiscally form via stellar evolution.

The photon sphere of a black hole is NOT analagous to the photosphere of a star. The photon sphere of a black hole refers to the last possible orbit around the black hole, whereas the photosphere of a star is where it is no longer transparent.

18. Jun 26, 2004

### Orion1

Oppenheimer Oppression...

jcsd, what you have stated is true, however are still missing my point, I am only presenting a demonstration between the density of a BH and a neutron star with an equal mass. I have not inferred nor indicated that a neutron star with this mass will collapse into a BH. The mass selected is arbitrary only for convenience.
A black hole of a mass of about 1.4 solar masses could not realtiscally form via stellar evolution.

A BH with a Chandrasekhar mass can form through Hawking Radiation evaporation from a more massive BH, though the process is extremely slow.

The topic is the density of a black hole, not electron or neutron degeneracy.

The photon sphere of a black hole is NOT analagous to the photosphere of a star.

I was not attempting to make such an analogy, only stating that avoiding such contractions in physics is impossible. It is implied that a BH photosphere IS a photon sphere and NOT an analogy to a solar photosphere.

I was not attempting to demonstrate stellar evolution, only a demonstration of comparative mass densities.

The neutron degenerancy mass is called the Oppenheimer Mass Limit for a neutron star.

Oppenheimer Mass Limit:
$$M_o = 3M_\odot$$

The radial solution for a spherically symmetric Oppenheimer BH sphere horizon is:
$$r_o = \sqrt[3]{ \frac{3 M_o}{4 \pi \rho_o}}$$

The radial Schwarzschild Solution for a spherically symmetric gravitational BH event horizon is:
$$r_s = \frac{2 G M_o}{c^2}$$

QM/classical GR shutdown:
$$r_o = r_s$$

$$\sqrt[3]{ \frac{3 M_o}{4 \pi \rho_o}} = \frac{2 G M_o}{c^2}$$

Oppenheimer Density Solution for spherically symmetric gravitational Oppenheimer BH:
$$\rho_o = \left( \frac{3c^6}{32 \pi G^3 M_o^2} \right)$$

Based upon the Orion1 Equasions:

What are the radius and density values of a Oppenheimer neutron star with a Oppenheimer Mass?

What are the radius and density values of a Oppenheimer BH with a Oppenheimer Mass?

What are the classical Schwarzschild radius and density values for a Schwarzschild-Oppenheimer BH?

---
jcsd, this approach, although more realistic for stellar evolution, does not simplify my argument for comparative densities of equivalent masses.

Last edited: Jul 1, 2004
19. Jun 26, 2004

### jcsd

I don't see the relevnace tho' to the topic, the 'density' of a balck hole is usually measured from it's event horizon, out of interest the radius of a Scwarzchild black holes photon sphere is simply:

$$\frac{3GM}{c^2}$$

I'm not sure you can say that the black hole has any kind of photosphere as that is to do with the optical properties of a star, I suppose the venet horizon would be the nearest analogy to a photosphere.

20. Jun 26, 2004

### Labguy

The "density" of a BH isn't measured from its event horizon. We can't see or measure an event horizon radius. The only way we can arrive at an Rs is to know the BH mass. From the mass we use the classical $$\frac{2GM}{c^2}$$ to get the Rs, and, as you stated, $$\frac{3GM}{c^2}$$ for the photon sphere. As an aside, the "Oppenheimer" limit (there are several other names too) is 3.2 Ms instead of the 4 mentioned in an earlier post.

And, knowing the mass, therefore the EH and photon sphere radius, still tells us nothing at all about density of or in a BH since the EH is simply an "area of influence" defined by the math above. Density is and would be where there is a measurable quantity of matter (the mass) and a defined volume, Planck size or larger. As Integral mentioned in an earlier post, no sense guessing because we don't have the means to peer inside any Event Horizon for any information at all other than that it exists.

Lastly, since there can be no "static" (non-rotating) black holes, why do the excercises in static math, unless it is a fun or practice thing?