Must a black hole be a point singularity?

[Ich]

Please, get your units fixed. Density is not kg/m^2. Pressure is also not kg/m^2. Your formula gives N/m^2.
BTW, radiation pressure is \rho c^2/3, I forgot the factor 1/3 in my previous posts.

 

[Bernie G]

Thank you. I did it again! The sentence above should have read: Using the Wiki reference http://en.wikipedia.org/wiki/Neutron_star , neutron density near the center of a typical neutron star core might be 7 X 10^17 kg/m^3.

For pressure, why not use kg/m^2 , to be consistant with the Wiki neutron star article?

Where did you get the formula radiation pressure = (pc^2)/3 ?

 

[Ich]

For pressure, why not use kg/m^2 , to be consistant with the Wiki neutron star article?

Because pressure has units kg/m/s² = J/m³ = N/m², not kg/m². I don't see where Wiki uses a different notation.

Where did you get the formula radiation pressure = (pc^2)/3 ?

You can find it http://en.wikipedia.org/wiki/Photon_gas" , for example. Basically, it means that the kinetic energy of the photons is evenly distributed over the three directions of motion, while the two directions perpendicular to a given surface obviously don't contribute to the pressure on that surface. So only one third of the energy contributes to pressure.

 

[JaredJames]

Bernie, pressure is force per unit area. Mass is not a force. The force 10kg applies to a body on Earth is not the same as it would apply on the moon. To use mass doesn't really mean anything unless you are working in a specific gravity (or constant acceleration for better description) field. It works on Earth because you can assume constant accelerating force at all points on the surface.

10kg/m^2 on Earth is not the same pressure as 10kg/m^2 on another planet / moon / star etc.

You should use the SI units.

 

[Bernie G]

Yes, my math may be wacky... but that might not matter if my wacky misconceptions for calculating pressure in a neutron star are consistent with my wacky misconceptions for calculating pressure in a black hole.

If essentially all the matter in a black hole converts to radiation because of insanely high temperatures, that radiation should exert a pressure. That radiation pressure, whether it is (pc^2)/3 or pc^2, is still without limit and should provide a support mechanism.

 

[nismaratwork]

Yes, my math may be wacky... but that might not matter if my wacky misconceptions for calculating pressure in a neutron star are consistent with my wacky misconceptions for calculating pressure in a black hole.

If essentially all the matter in a black hole converts to radiation because of insanely high temperatures, that radiation should exert a pressure. That radiation pressure, whether it is (pc^2)/3 or pc^2, is still without limit and should provide a support mechanism.

Maybe, and I'm just spit-balling here... it's time to get off the wacky train?

 

[Bernie G]

Do you think its logical that essentially all the matter in a black hole should convert to radiation because of the insanely high temperatures, and the radiation pressure, whether it is (pc^2)/3 or pc^2, is still without limit and should provide a support mechanism?

 

[nismaratwork]

Do you think its logical that essentially all the matter in a black hole should convert to radiation because of the insanely high temperatures, and the radiation pressure, whether it is (pc^2)/3 or pc^2, is still without limit and should provide a support mechanism?

I think you're right about the radiation, but as has been mentioned before, once you're inside the event horizon it ceases to be a viable support mechanism. All paths within the EH lead to eventual collision with the singularity, and the notion of radiation pressure being supportive simply no longer applies.

 

[JaredJames]

Pressure has a force as a component, force has an acceleration component. If you do not have that acceleration component, you do not have force and so do not have any pressure.

10kg sat on a 1m^2 surface in space is = 10kg/m^2. However, there is no acceleration acting on the mass and so no force exerted by the mass on the surface. In other words no pressure. You can't use those units (kg/m^2) for anything other than in a constant acceleration situation (such as basic calculations on earth).

Wacky, I didn't describe them as wacky, I'm just requesting you use SI units for the reasons outlined above.

I have also read the wiki on neutron stars and would like to know where you see them using non-standard units? I didn't see kg/m^2 anywhere (please correct me if I'm wrong).

As nismar says, once inside the EH you are going to impact the singularity. The immense gravity means not even light can escape the EH so no amount of pressure from radiation is going to stop that.

 

[Bernie G]

When one boldly goes where no one has gone before, it sometimes helps to close one eye. Sometimes it might help to close both eyes.

 

[JaredJames]

Nismar, I'm getting nasty Nam flashbacks here. It's the clamshell riddler all over again. Quick need to eject whilst I have the chance!

Bernie on a more serious note, at least try to use SI units to see if your hypothesis fits.

Sometimes it might help to close both eyes.

Going in blind is the quickest way to walk into something you would have otherwise seen!

Let's assume you're correct, wouldn't the radiation pressure work equally in all directions, therefore cancelling itself out?

 

[Bernie G]

I don't agree with a singularity yet. IF there is a spherical distributed mass of radiation, the gravitational force near the center is relatively trivial, and the gravitational force increases as R increases, becoming so high at the Schwarzschild radius that radiation can not escape. But that doesn't mean the sphere of radiation collapses on itself, if there is a support mechanism stronger than gravity. Its just that radiation can't escape the sphere of radiation.

 

[nismaratwork]

Nismar, I'm getting nasty Nam flashbacks here. It's the clamshell riddler all over again. Quick need to eject whilst I have the chance!

Bernie on a more serious note, at least try to use SI units to see if your hypothesis fits.


Going in blind is the quickest way to walk into something you would have otherwise seen!

Let's assume you're correct, wouldn't the radiation pressure work equally in all directions, therefore cancelling itself out?

Ahhhh, not he-who-shall-not-be-named! I think Bernie G isn't there however (thank god), just trying to get the notion of how things work in a really strange region.

Bernie: He's right about the SI units you know... it's like agreeing on semantics before a debate... it smooths the way greatly.

 

[JaredJames]

Aside from within the singularities mass*, I was under the impression gravity decreased with radius from the mass? I may well be wrong on this, but it would be interesting to know why it would increase up to the EH and then decrease from that point on as you are implying. Or is this where the Schwarzschild radius comes in (I don't know what that is, shall use Google)?

(*as with the earth, the deeper you go the lower the g pulling you towards the centre)

 

[Bernie G]

"wouldn't the radiation pressure work equally in all directions"

Gas pressure in a star works in all directions.

 

[Bernie G]

"as with the earth, the deeper you go the lower the g pulling you towards the centre"

Yes, with a distributed mass.

 

[nismaratwork]

I don't agree with a singularity yet. IF there is a spherical distributed mass of radiation, the gravitational force near the center is relatively trivial, and the gravitational force increases as R increases, becoming so high at the Schwarzschild radius that radiation can not escape. But that doesn't mean the sphere of radiation collapses on itself, if there is a support mechanism stronger than gravity. Its just that radiation can't escape the sphere of radiation.

Look, many people don't believe that a full theory describing quantum gravity will leave a singularity, but in the current context that's what we're dealing with. The alternatives are NOT what you're describing, because even in theories where no singularity exists (string theory for instance), radiation pressure is no longer an issue. The notion of the space and time within the EH being anything like that outside is what's leading you to believe that radiation pressure even MATTERS. One way or another, the worldline of each quanta of energy is either crashing into a singularity, or being rendered into fuzzballs or the like, and there is reason to believe that the EH isn't the point at which those effects begin.

As others have said, you could pass the EH of an AGN and not even notice that you'd done so. The EH is not some skin containing pressure, it's just a demarcation point with drastic consequences for the fate of anything past it.

 

[nismaratwork]

"wouldn't the radiation pressure work equally in all directions"

Gas pressure in a star works in all directions.

At some point the radiation no longer has as many degrees of freedom that it would in a classical body outside of the black hole... this is why everyone here keeps coming back to the inevitable "crash" into a singularity, or fuzzball... or whatever is there. The closer that the radiation comes to the center of this mass, the fewer degrees of freedom it has, and at any rate, once it crosses the EH there is nothing leading out of the EH. You don't get the same chaotic 'motion' in such a restrictive space that you do in the rest of the universe.

 

[Bernie G]

Yup, radiation doesn't get out of the black hole, if you want to call that a degree of freedom. Gravity is interesting... it gets out of a black hole and in other ways does not act like radiation. String theories ... fuzzballs ... conventional physics ... which would you prefer?

 

[Ich]

Bernie G,

I don't know what you're arguing here. There's this http://books.google.de/books?id=UzISeBGrUSYC&pg=PA692&dq=buchdahl%27s+theorem&hl=de&ei=VuWlTKCDOMjBswac3Im3CA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDMQ6AEwAQ#v=onepage&q&f=false" that proves that anything, matter or radiation must collapse if you put enough energy in a given space. That's it.
I know you can't follow the proof mathematically, that's why Igave all these explanations like pressure gravitating, photon gases being unstable, or, most stringently, the spacetime geometry inside the horizon.
If you take GR for granted, this is what happens. You can understand it or not, but you just can't use handwaving Newtonian intuition to reject this outcome. There is nothing stronger than gravity inside the horizon. Can't be.
Whether there is a real singularity or is something completely different, we know that we can't trust GR at the highest densities.

 

[Bernie G]

I certainly agree that the gravity from a massive enough sphere of radiation can contain that radiation. I don't buy that gravity causes that sphere of radiation to collapse to point.

Einstein didn't believe in a point singularity. We should consider his opinion on anything related to conventional physics or GR or whatever. If a theorem proves it for you I can respect and value that position but I don't have to believe it.

 

[nismaratwork]

I certainly agree that the gravity from a massive enough sphere of radiation can contain that radiation. I don't buy that gravity causes that sphere of radiation to collapse to point.

Einstein didn't believe in a point singularity. We should consider his opinion on anything related to conventional physics or GR or whatever. If a theorem proves it for you I can respect and value that position but I don't have to believe it.

From what I understood you've been arguing that the mechanism which keeps a singularity from forming is radiation pressure, which is what everyone is trying to explain makes no sense. If you simply assert that a singularity is probably an artifact of a breakdown of GR at that point (and any theory really) I don't think you'll find much argument.

 

[Bernie G]

You said there is nothing stronger than gravity inside the horizon. Kind of true. I'm saying in a sphere of radiation, pressure driven by density will increase faster than gravity until you reach the surface of the sphere. Containment is achieved at the surface of the sphere when the gravitational force has increased to the point where it contains radiation. I don't think this requires the sphere to collapse.

 

[Ich]

I'm saying in a sphere of radiation, pressure driven by density will increase faster than gravity until you reach the surface of the sphere.

But surely you understand that you are in no way qualified to make such a statement? That's not a problem, I mean, all of us are not qualified to make strong assertions in most fields of science or even daily life. But then, most of us don't come to, say, the egyptology forums claiming that these faroahs surely built their cones upside down.

If a theorem proves it for you I can respect and value that position but I don't have to believe it.

Of course you have to believe it. Mathematical theorems are not points of view. This is not humanities here.
Further, as nismaratwork said, no theorem within GR could prove the existence of a point singularity, as this is exactly where GR breaks down. Nobody here claimed the existence of a point singularity.
All we're saying is that, in the context of GR, radiation cannot halt the final collapse.

 

[Bernie G]

Was Einstein qualified? He didn't believe it.

 

[JaredJames]

We are very close to bordering on personal theories here.

You said there is nothing stronger than gravity inside the horizon. Kind of true.

Why is this "kind of true"? Do you have evidence which says otherwise? If so, please do cite it. (Again, this may come down to my own lack of understanding here so if anyone can tell me of something stronger than gravity I would be very interested.)

Einstein produced a series of theories which can be shown to be mathematically correct. You are making little more than assumptions based on your own potentially misguided understandings. Are you really comparing yourself to Einstein?

 

[Ich]

Was Einstein qualified? He didn't believe it.

He didn't believe what? References?
Most people don't like that GR leads to singularities. So what?

Now please make your point:
1. You don't believe the theorems and all the fancy maths that prove you are wrong
2. You question the validity of GR within its region of applicability
3. ...?

You know, 1. and 2. are no options here at PF.

 

[Bernie G]

Question: If somehow 1,000,000 kilograms of matter was contained in 1 cubic centimeter, and this matter was entirely converted into energy, and somehow contained in the 1 cubic centimeter, what do you think the pressure would be? Any thoughts would be welcome.

 

[JaredJames]

Well I get 9.0x10^22 Joules for the energy value. (Using c = 3.0x10^8m/s).

Now I assume you've just gone E = PV and rearranged to give you the volume, which I get to be 9.0x10^24 Pa.

Somehow, I feel there is something wrong with the maths there.

 

[Bernie G]

Yes, it might be better if the calculation was all in meters. New question: If somehow 1,000,000,000,000,000 kilograms of matter was contained in 1 cubic meter, and this matter was entirely converted into energy, and somehow contained in the 1 cubic meter, what do you think the pressure would be?