# Black hole question

1. Nov 3, 2005

### Psi 5

I am assuming that some current theories believe that there is a singularity inside a black hole.

My question is this. Would there be a way to tell if the matter in a black hole was a singularity or not? Would there be a difference?

My guess is that there should be some observable difference if the matter had volume and was not a singularity. Like maybe the diameter of the event horizon.

2. Nov 3, 2005

### Danger

As far as I know, the singularity is what defines a black hole. I've never seen anything that would allow for a >c escape velocity without one. I'm not all that 'up' on the subject, though.

3. Nov 3, 2005

### Spin_Network

There is a contention that if particles are emminating from a BH then there is NO singularity, its the concept of Singularity that "traps" anything that encounters it?

4. Nov 4, 2005

### hellfire

As far as I know there are singularity theorems in general relativity which state that the existence of an event horizon is always related to the existence of a singularity behind it. This means that if there is no singularity then no event horizon will exist. Thus if one could observe the event horizon one would know about the existence of the singularity. This could be achieved indirectly detecting Hawking radiation which is very faint. However, being more realistic I guess one has to rely on the estimations of the mass of the object to know whether there exists a singularity or not. If the mass is greater than the Oppenheimer-Volkoff limit, then general relativity predicts a black hole (and therefore an event horizon and a singularity) instead of a smooth distribution of matter.

5. Nov 4, 2005

### franznietzsche

The even horizon is not a physical surface. It does not exist physically anymore than the sphere that our GPS satellites orbit on around the earth. All the matter is concentrated in the singularity.

6. Nov 4, 2005

### Psi 5

I don't see the need for a singularity to create an event horizon, just a certain amount of gravity. Are you saying that if enough matter is gathered in one spot that exceeds the theoretical mass required to create an event horizon and no singularity is formed then no event horizon is formed? That doesn't seem right.

7. Nov 4, 2005

### Danger

I just don't see how enough mass to form an event horizon can avoid the gravitational collapse into a singularity, even if it happens after the horizon is formed.

8. Nov 4, 2005

### Labguy

True about the EH, but all we really know about the mass is that it is inside the influence "sphere" of the EH.
I agree with this 100%. There is less insistence on the need for a singularity than there was just a few years ago. Even Quark Stars are being discussed again by physicists at the Harvard-Smithsonian Center for Astrophysics, among others. I copied a recent blurb to Wordpad so I don't remember the source.
So, if we consider Quark stars, who has yet published the degree of compression it would take? Is it possible that the mass compressed into a quark star could be enough to fall within 2GM/c2 ? Either of these warrant consideration? I think so, and maybe stars of the more massive Top Quark, much more massive than the other 5 types.
http://www.iop.org/EJ/article/1367-2630/4/1/314/nj2114.html
http://spaceflightnow.com/news/n0204/11newmatter/
....

9. Nov 5, 2005

### hellfire

May be I misinterpreted the singularity theorems, but my current understanding does not allow me to agree with this. Take for example http://www.absoluteastronomy.com/encyclopedia/p/pe/penrose-hawking_singularity_theorems1.htm [Broken] rough formulation of one of the singularity theorems of Hawking and Penrose:

We only have to agree that an event horizon is a trapped null surface (as far as I know it is) and we will conclude that event horizons always have (under realistic conditions) singularities within them. This is described with more detail in Wald's GR book pp. 239 - 241 (also a definition of trapped surface is given there).

To argue that there can be mass within it's Schwarzschild radius, that without a singularity leads to a body from which light does not escape, seams to me a "newtonian" argument that might not be necessarily valid.

I would appreciate corrections if I misunderstood this.

Last edited by a moderator: May 2, 2017
10. Nov 5, 2005

### Psi 5

I'm not a physicist. I don't know what a null surface is. What I do know is that an event horizon is nothing more than the point in a field of gravity where the force of gravity exceeds a certain level. This level can be exceeded by the presence of a certain amount of matter whether it collapses or not.

My contention is that if that certain amount of matter is present there should be some observable difference between the matter being a singularity or not, like the diameter of the event horizon.

11. Nov 5, 2005

### pervect

Staff Emeritus
Where did you get this defintion of an "Event horizon"? This does not match anything I've read. See for instance the Wikipedia defintion of an event horizion

http://en.wikipedia.org/wiki/Event_horizon

Wald's defintion of "Event horizon" in "General Relativity" is much more technical, but it also involves the ability of light to escape "to infinity".

MTW doesn't list "Event horizon" in the index (I suspect it's mentioned somewhere in the 1200 pages, but I don't recall where exactly - the poor indexing of the book is a chronic problem).

I can't find my copy of Taylor & Wheeler "Black Holes & Time Warps" which would probaly have a good non-technical defintion of the term.

Anyway, I've looked at serveral sources, and none of them are at all similar to your defintion of "event horizon", which I think is incorrect.

12. Nov 5, 2005

### pervect

Staff Emeritus
Global methods in GR are unfortunately one of my weak points, but as Hellfire mentions it has in fact been proven that given a number of reasonable assumptions, black holes in fact must contain singularities.

Probably the most arguable of these assumptions is the non-existence of exotic matter, i.e. the statement that matter obeys the "strong energy conditions".

If one has exotic matter, it would be possible to imagine a black hole containing a core of exotic matter (with pressure exceeding its density) supporting normal matter with a positive energy density that satisfies the "strong energy condition", creating a black hole that has an event horizon without a central singularity.

Without exotic matter, the singularity theorems apply and show that according to the laws of GR, black holes must contain singularities. At least that's my understanding. This statment only applies to GR, I believe quantum gravity can still avoid the existence of true singularities.

13. Nov 5, 2005

### hellfire

Thank you for the clarification pervect. Singularity theorems are often formulated in very technical terms. I have found a slide-set for black hole lectures http://www.physics.nus.edu.sg/einstein/lect10/lect10.ppt [Broken] in which this is stated in very easy and clear terms (see slide nr. 17):

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14. Nov 5, 2005

### Psi 5

Here is a definition I found in a dictionary:

"The region, usually described as spherical, marking the outer boundary of a black hole, inside which the gravitational force is strong enough to prevent matter or radiation from escaping."

That sure sounds like what I said.

15. Nov 5, 2005

### Danger

Keep in mind, though, that a dictionary is not a physics text. Their definitions are geared to the general public with barely a passing interest in the subject, such as someone reading a newspaper article or doing a puzzle. As an example of that, the event horizon is not the outer boundary of a black hole... it's the inner one.

16. Nov 5, 2005

### Psi 5

You have lost me.
Fact: gravity can bend light. This has been observed.
Deduction: enough gravity can trap light.
Deduction: a certain amount of matter can create that amount of gravity
Deduction: enough matter can be in one place to exceed that amount
Deduction: since we don't know singularities exist, that amount of matter may or may not be a singularity but will not be limited to the amount of gravity it produces

According to you guys at least one of those deductions is wrong. It sounds like you are saying if there is no singularity then there is an upper limit to gravity no matter how much matter is there and that limit is less than the amount needed to trap light or no amount of gravity can trap light without a singularity.

Unfortunately I don't have Powerpoint to watch that slide show.

Last edited: Nov 5, 2005
17. Nov 6, 2005

### hellfire

General relativity is not easy and may defy "common sense" (based on newtonian conception of gravity) sometimes. The "amount" of gravity you are looking for, is given only by the existence of a singularity. Otherwise you will get no event horizon. This is the claim of that singularity theorem.

18. Nov 6, 2005

### Jonny_trigonometry

The event horizon is just the radial distance from the center of mass where the speed of light is the escape velocity, and the radius of the object does not extend beyond this radius. Then all particles have an event horizon by that definition if you solve with newtonian gravity, so that makes me ask a question. Is there some radial distance and/or some mass where GR fails to compute the even horizon? Does this have anything to do with the uncertainty principle?

19. Nov 6, 2005

### Danger

My contention here is that you cannot assemble that much mass in one place without it collapsing into a singularity due to its own gravity.

Can't help with your question, Jonny. It's way beyond me.

20. Nov 6, 2005

### pervect

Staff Emeritus
Last edited by a moderator: May 2, 2017
21. Nov 6, 2005

### pervect

Staff Emeritus
Note that this doesn't mean a strong "field". A very weak field that does not drop off with distance can also trap light. That's one of the weaknesses in the dictionary defintion you posted, it's a bit misleading on this point. Thinking about the "escape velocity" being greater than or equal to 'c' gives a less misleading picture than your dictionary defintion.

So far so good.

There are reasons for beliving that normal matter cannot support a pressure (force/unit area, energy/unit volume) greater than c^2 times its density (mass/unit volume). The c^2 is a unit conversion factor. This is known as the "strong energy condition" and comes from requiring that the energy density term in the stress-energy tensor always be positive in any frame of reference.

What the singularity theorem says is that assuming the strong energy condition is true, matter can not be strong enough (have a high enough pressure) to keep itself from collapsing under its own weight when you collect enough of it together to form an event horizon (black hole).

Because pressure cannot halt the collapse, the final state of any such collection of matter will be a singularity.

22. Nov 8, 2005

### franznietzsche

The thing is, its physically impossible for that much matter in that little space to not collapse into a singularity.

What you're describing is not physically possible. The amount of matter necessary to generate an event horizon will always collapse into a singularity.

You're trying to apply newtonian thinking to a strictly non-newtonian problem. Essentially high school physics to what is a grad school level problem.

You cannot use newtonian gravity with black holes. Period. It fails, completely in that regime. If you tried to calculate even horizons you suggest you would get event horizons inside the particles, which would be wrong, since once you're inside an object, the standard gravitation force equation no longer applies and the situation is much more complex. This has nothing to do with the uncertainty principle. You cannot use newtonian gravity to calculate things in General Relativity regime. Its like explaining how humans walk with their wings. It just doesn't make any sense. The two are based on drastically different assumptions, and are only in agreement when those differences are negligible. Black holes are a phenomenon where they are definitely NOT negligible.

And as Danger pointed out its not really correct (Wow, Danger you just keep impressing me more and more with what you've learned here).

Yes

Yes
Yes, but poorly worded. Sufficient matter can bend space enough to trap light. However, that must occur outside of the object, as the gravitational field weakens once you are inside of an object (because some of the mass pulls outward, not inward).

Yes
No. Singularites are mandated by the same principles that make the previous statements true. if those are true (in the form of our current theories) singularities have to exist. And by those same theories, only the singularity can form the even horizon. You are trying to seperate things that are closely linked. The fact that a singularity is the only thing that can produce an event horizon is a consequence of the same things that make the above statements true. So if the above statements are true (or rather, if our theoretical derivation of them is true, meaning we didn't get the right answer the wrong way, like Bohr did) then only singularities can produce event horizons.

Yes.

23. Nov 8, 2005

### Danger

Thanks.
I have learned a tremendous amount about almost everything since joining. Actually, though, this isn't one of them. I wrote a technical article on black holes for a major newspaper in '79. Unfortunately, I've forgotten most of what I knew then.

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