Must a black hole be a point singularity?

[Bernie G]

If during star collapse the mass not blown away is large enough to form a black hole, shouldn’t the resulting extraordinary high temperature essentially convert all the mass into contained radiation? The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the equivalent mass density of the radiation). This should prevent collapse to a singularity since this radiation pressure has no limit and increases as density or 1/R*3, faster than the increase of gravitational force.

(format test only: c squared = c*2 = c² )

 

[nismaratwork]

If during star collapse the mass not blown away is large enough to form a black hole, shouldn’t the resulting extraordinary high temperature essentially convert all the mass into contained radiation? The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the equivalent mass density of the radiation). This should prevent collapse to a singularity since this radiation pressure has no limit and increases as density or 1/R*3, faster than the increase of gravitational force.

(format test only: c squared = c*2 = c² )

GR equations say, "yes" it must be a singularity, but there are certainly doubts. I think many believe that a workable framework of quantum gravity will eliminate the singularity from the equations, and our understanding of nature.

 

[Hurkyl]

The singularity is "off the map", so to speak -- it doesn't have any shape itself, but we can talk about how the space around where it would be is defective.

The space around a point-like hole has the same shape as the space around a ball-like hole -- there isn't really any difference between the two.


(I think other shapes are possible -- e.g. a ring shape. The space around a ring-shaped hole really does look different than the space around a point-like hole)



It's easy to see in two dimensions with polar coordinates. Normally, the set of all (r,theta) with r > 0 form a plane with a single point removed -- the origin.

Now, do a change of coordinates, setting s = r + 1. Plotting the (s,theta) as polar coordinates now reveals an entire closed disk removed from the plane.

The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the equivalent mass density of the radiation). This should prevent collapse to a singularity since this radiation pressure has no limit and increases as density or 1/R*3, faster than the increase of gravitational force.

Well, remember this is GR, not Newtonian gravitation. High pressure accelerates the collapse -- that is why a black hole can form in the first place! (at least, as I understand things)

 

[Bernie G]

I think the question basically is: Can intense radiation pressure be the support mechanism inside a black hole? I think it is logical that when a star above several solar masses collapses, the neutrons in the core disintegrate into radiation and some quark matter. As the collapse continues and temperature rises still further virtually all matter converts to radiation. If the radiation is contained in the system, the pressure of the radiation should be P = pc*2 , where p is the equivalent mass density of the radiation. The contained radiation, which has mass, basically acts like a compressed gas that can generate pressures exceeding neutron collapse pressure.

As I understand the TOV equation, dP/dr is proportional to p + P, which means if P is high enough there is runaway collapse. I don't think Einstein accepted this equation because he didn't believe in a point singularity.

 

[nismaratwork]

I think the question basically is: Can intense radiation pressure be the support mechanism inside a black hole? I think it is logical that when a star above several solar masses collapses, the neutrons in the core disintegrate into radiation and some quark matter. As the collapse continues and temperature rises still further virtually all matter converts to radiation. If the radiation is contained in the system, the pressure of the radiation should be P = pc*2 , where p is the equivalent mass density of the radiation. The contained radiation, which has mass, basically acts like a compressed gas that can generate pressures exceeding neutron collapse pressure.

As I understand the TOV equation, dP/dr is proportional to p + P, which means if P is high enough there is runaway collapse. I don't think Einstein accepted this equation because he didn't believe in a point singularity.

The only viable alternative to collapse into a singularity that exists in theory now, comes from String Theory... and that's not exactly coming with the developed pedigree of GR or QM. Given the "black" nature of the hole, it's probably best to concern ourselves with the event horizon on out.

 

[JaredJames]

it's probably best to concern ourselves with the event horizon on out.

Oh no not the event horizon again. I'm still having nightmares about the last thread on this!

 

[Chronos]

A singularity is a red flag in physics. It strongly suggest the mathematical model has 'broken' when singularities emerge in the solution. We know this for fact in GR, and suspect the same in QM. Reconciling GR and QM [quantum gravity] will give us a better idea how nature deals with her dirty laundry. I think we will ultimately arrive at a theory that transcends both GR and AM. Ptolemy's epicycles persisted for about 1500 years before we finally overturned that theoretical apple cart.

 

[Bernie G]

Yup, present theories could push people over the edge. If a neutron star collapses to perhaps one tenth its volume, wouldn't we expect a dramatic increase in temperature? Wouldn't essentially all matter be converted to radiation? Matter changes dramatically above the temperature of quark production. Below this temperature we have matter with little energy; above this temperature we have radiation with little matter. Therefore above this temperature we should analyze the characteristics of radiation instead of matter.

How would a huge distributed mass of radiation react to itself gravitationally? At the center of the distributed mass we would expect little gravitational force, only intense pressure. Gravitational forces would increase with radius, reaching a point where they would be strong enough to contain radiation, acting like the skin of a balloon. Schwarzschild radius.

 

[twofish-quant]

The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the equivalent mass density of the radiation). This should prevent collapse to a singularity since this radiation pressure has no limit and increases as density or 1/R*3, faster than the increase of gravitational force.

Doesn't help you. Remember that E=mc^2, so any radiation that you have also has mass, which means that it also has gravity.

I'll leave it for you as an exercise, but you can show that if you have enough mass-energy in a small enough space, that the gravity created by that radiation is increase faster than any radiation pressure. The more radiation you have, the more gravitational force and once you hit some limits, then more radiation *increases* the collapse.

 

[twofish-quant]

If a neutron star collapses to perhaps one tenth its volume, wouldn't we expect a dramatic increase in temperature?

Yes.

Therefore above this temperature we should analyze the characteristics of radiation instead of matter.

Yes, and this is a bad thing if you are trying to halt a collapse. I give you a table made of wood. You jump on it, and the table stops you. If I give you a table made of laser light, and you jump on it, the laser light won't stop you.

So the fact that the temperatures increase to the point where things start behaving like radiation is exactly why things collapse.

How would a huge distributed mass of radiation react to itself gravitationally?

Something that helps a lot is to just think of matter and radiation as the same thing. I have a pound of brick. Now suppose I turn it into energy by maybe combining it with a pound of anti-matter. The two pounds of photon gas *still* has the same gravitational pull.

The way that people model this is to just model radiation as a photon gas, and just like any other gas, photon gas has weight and gravity. So what happens if I turn neutron star material into photon gas is that the gravity stays the same, but the pressure goes way down.

At the center of the distributed mass we would expect little gravitational force, only intense pressure.

Nope. E=mc^2. If you have a lot of E, you will still have a lot of m.

 

[Ich]

I give you a table made of wood. You jump on it, and the table stops you. If I give you a table made of laser light, and you jump on it, the laser light won't stop you.

Well, if you turn the whole table into radiation, it will most certainly stop you. Actually, it will accelerate the particles that once were you away at a significant fraction of the speed of light. Kind of total protonic reversal.
It's a good idea to get a much pressure as possible, if you don't mind the side effects. But it doesn't help.

Something that helps a lot is to just think of matter and radiation as the same thing. I have a pound of brick. Now suppose I turn it into energy by maybe combining it with a pound of anti-matter. The two pounds of photon gas *still* has the same gravitational pull.

Actually, pressure gravitates, which means that radiation has the double gravitational pull.
Radiation is unstable, it will either explode or contract to a "singularity". It can be proven that it will contract if it is enclosed in less that 9/8 of its Schwarzschild radius.

 

[Bernie G]

"At the center of the distributed mass we would expect little gravitational force, only intense pressure."
"Nope. E=mc^2. If you have a lot of E, you will still have a lot of m."

At the center of the Earth there is relatively trivial gravitational force, only intense pressure. Same with a neutron star.

 

[Bernie G]

"I give you a table made of wood. You jump on it, and the table stops you. If I give you a table made of laser light, and you jump on it, the laser light won't stop you."

If 1 gram of matter is contained in 1 cc, and then is totally converted into radiation, and this radiation is contained in the 1 cc, the expected pressure would be pcˆ2 = 10ˆ21 g/cmˆ3.

 

[Ich]

p= \rho c² = 10^14 J/cm³=10^20 Pa.

 

[Bernie G]

Good, the kind of response I was looking for. I should have titled this thread instead "Can radiation pressure be the support mechanism inside a black hole?"

Also I should have written 10^21 grams/cm^2 above, not 10^21 g/cm^3.

Lets call pressure P, density = p = rho, volume V, mass m, light speed c.

P would be the expected amount of radiation pressure in a closed system when mass is converted to radiation. Pressure, normally defined as F/A, also equals (available energy)/volume. If m is the amount of mass converted to radiation in a closed volume V, then P = mc^2/V. Since p =m/V, then P = pc^2. 1 gram of radiation contained in 1 cc would equal 9 X 10^20 gm/cm^2.

 

[Bernie G]

Better phrased: 1 gram of radiation contained in 1 cc would create a pressure of 9 X 10^20 grams/cm^2.

Its unconventional, but I think people should get used to saying grams or kilograms of radiation.

 

[Ich]

I can follow all your steps except this one:

1 gram of radiation contained in 1 cc would equal 9 X 10^20 gm/cm^2.

1 g * c² = 10^14 J (well, 9*10^13). So there's 10^14 J/cm³ = 10^20 Pa.

What you seem to be doing is you take c in units of cm instead of m, and then claim that the so dereved unit of energy (actually 10-4 J) is grams. That doesn't work.

EDIT: I just saw your second post and thus looked more closely. You're now talking about g/cm² as a unit of pressure. Don't do that. g/cm³ is non-SI, and it uses c=1, but at least it makes some sense.

 

[stevebd1]

It's worth pointing out that geodesics become space-like within 2M (the Schwarzschild radius) so no matter how high the pressure is, unless geodesics are time-like within the collapsing matter (which I'm guessing when applying the Schwarzschild interior solution for masses that fall within 2M isn't the case) then a stable radius cannot be sustained within 2M regardless of the pressure, it would be like us hovering at 1.00 pm in time-like geodesics, it's just not going to happen. For the Schwarzschild solution, the only way the collapse can stop is if the energy that separates matter and space become indistinguishable and geodesics as we understand them become something different which is what is supposed to happen at Planck scale/density.

 

[Bernie G]

I will probably restart this thread tomorrow with the title: "Can radiation pressure prevent collapse inside a black hole?"

 

[Bernie G]

Ich, so we are on the same page, how would you prefer all of us to refer to pressure?:

kg/m^2

or kg/square meter

or ?? ... your suggestion

Also, how would you prefer us to density? We can have a better discussion if we all use the same units and terminology.

 

[JaredJames]

Any reason you don't like Pa? It's the SI unit after all.

kg/m^2 is non-SI and I don't see why you want to use it.

 

[Ich]

how would you prefer all of us to refer to pressure?

I'd prefer very much if we'd all use at least Force per Area, not Mass per Area. You may choose units as you see fit, but of course SI or geometric units are preferred in a physics forum.
I'm told that there are some regions - like Myanmar or Liberia - where the locals still use strange units like lb, and that in these regions it is also common to use the weight of such a mass as a measure of force, like lbf. But there's no such tradition in the developed world(*), where the unit of force was the pond until SI became standard.
So lb/in² or g/cm² are no go, lbf/in² or N/cm² are at least not wrong, and N/m² or 1/m² are ok, depending on the context.

(*)SCNR, no offence!

 

[Ich]

It's worth pointing out that geodesics become space-like within 2M

I think you're talking about worldlines. Worldlines are timelike geodesics, and they stay timelike within 2M. It's just that the Schwarzschild t and r coordinates swap character in the interior region, but that doesn't affect physics. It's instructive, however, as r becomes a past-oriented time coordinat, which means that becoming older = going to smaller r.

However, every timelike or null (i.e. radiation) geodesic in the interior region will abruptly end after a finite proper time at the singularity. Pressure doesn't help, there simply is no outward direction inside the horizon.
"Outward" is not a spatial direction, it's the past. You can't go there.

 

[Bernie G]

kg/m^2 is best.

 

[Ich]

kg/m^2 is best.

Did you read https://www.physicsforums.com/showthread.php?p=2909119#post2909119"?

 

[nismaratwork]

Did you read https://www.physicsforums.com/showthread.php?p=2909119#post2909119"?

It couldn't be more clear that he didn't if he suggested "stone/fathom^2".

 

[Ich]

http://en.wikipedia.org/wiki/FFF_system"

 

[nismaratwork]

http://en.wikipedia.org/wiki/FFF_system"

That's a topper you're only going to find on PF!

 

[JaredJames]

http://en.wikipedia.org/wiki/FFF_system"

21 year old PF member runs to Google to find out what a firkin is!

 

[Bernie G]

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^2. If this density was converted to contained radiation, the expected pressure generated, pc^2, would be about 6 X 10^34 kg/m^2. Neutrons at that density can't exceed that pressure because E can't be greater than mc^2. Using the sloppy formula for neutron star core pressure -(GM^2)/R^4 gives about 1 or 2 X 10^34, sensibly somewhat less than than pc^2.

If the pressure at the core reaches pc^2, the core must collapse. Matter is converted to radiation, which then exerts a pressure of pc^2. Not that complicated.

 

[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.