Black Hole

[hellwing]

what will happen to matter if it is caught by black hole?

[DrP]

It will get sucked in and squished I expect. There was a thread about black holes started just yesterday!?...

[Pete]

what will happen to matter if it is caught by black hole?

Different observers will observe different things. Observers outside the black hole will observer the matter to approach the event horizon but never cross it. However these outside observers will eventually be unable to observe the matter due to an ever increasing red shift. An observer who is falling into the black hole will observe the matter to be torn apart by tidal forces. After that it gets nasty and eventually falls into the singularity and compressed into a point. Yuk!

 

Pete

[Royston]

what will happen to matter if it is caught by black hole?

 

I take it you've googled this question, before asking ?

 

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

 

http://cosmology.berkeley.edu/Education/BHfaq.html

 

http://hubblesite.org/explore_astronomy/black_holes/

 

There's also a search function on SFN. Black holes have been discussed a lot on here.

 

After that it gets nasty and eventually falls into the singularity and compressed into a point. Yuk!

 

Pete

 

Not that I'm an expert with black holes, but a singularity isn't a point.

Edited July 11, 2008 by Snail

[Pete]

Not that I'm an expert with black holes, but a singularity isn't a point.

That depends on the definition. E.g.

http://www.merriam-webster.com/dictionary/singularity

4: a point or region of infinite mass density at which space and time are infinitely distorted by gravitational forces and which is held to be the final state of matter falling into a black hole

In any case the singularity of a black hole is a point.

 

Pete

[Klaynos]

We can't comment really on the singularity because our physics breaks down

[Pete]

We can't comment really on the singularity because our physics breaks down

I assume you're joking?

 

Pete

[Klaynos]

I assume you're joking?

 

Pete

 

At the singularity you require a quantum theory of gravity, which we don't have.

[Royston]

That depends on the definition. E.g.

http://www.merriam-webster.com/dictionary/singularity

 

In any case the singularity of a black hole is a point.

 

Pete

 

But, as I'm sure you know, the Einstein equations breakdown at the singularity. If a singularity was a defined point, then it could be described by a co-ordinate system, but this isn't the case.

 

Besides, a singularity is a general mathematical term, I don't understand why people always associate singularities with solely black holes...probably not a good idea to use a dictionary for scientific terms, for obvious reasons.

 

Again, I'm not an expert, I havn't even started my GR course, just relaying what I've learnt from an expert.

[Pete]

But, as I'm sure you know, the Einstein equations breakdown at the singularity. If a singularity was a defined point, then it could be described by a co-ordinate system, but this isn't the case.

 

Besides, a singularity is a general mathematical term, I don't understand why people always associate singularities with solely black holes...probably not a good idea to use a dictionary for scientific terms, for obvious reasons.

Let us consult Wald's text on this topic. On page 214 Wald writes

Of course, our failure to describe a singularity as a "place" in precise mathematical terms does not in any way lessen the obvious fact that singularities exist in, say, the Robertson-Walker and Schwarzschild spacetimes. It simply means that we must find other ways to characterizing a singularity.

One needs to distinguish between the mathematical term and the physical term. The mathematical term for singularity is used to refer to points where a quantity goes to infinity as one approaches that point. A physical singularity is a mathematical singularity if it exists in all possible coordinate systems. If there is no physical singularity at a point then the singluarity is purely mathematical and is referred to as a "coordinate singularity."

Again, I'm not an expert, I havn't even started my GR course, just relaying what I've learnt from an expert.

It seems that the expert isn't Wald.

 

Pete

 

But, as I'm sure you know, the Einstein equations breakdown at the singularity. If a singularity was a defined point, then it could be described by a co-ordinate system, but this isn't the case.

 

Besides, a singularity is a general mathematical term, I don't understand why people always associate singularities with solely black holes...probably not a good idea to use a dictionary for scientific terms, for obvious reasons.

Let us consult Wald's text on this topic. On page 214 Wald writes

Of course, our failure to describe a singularity as a "place" in precise mathematical terms does not in any way lessen the obvious fact that singularities exist in, say, the Robertson-Walker and Schwarzschild spacetimes. It simply means that we must find other ways to characterizing a singularity.

One needs to distinguish between the mathematical term and the physical term. The mathematical term for singularity is used to refer to points where a quantity goes to infinity as one approaches that point. A physical singularity is a mathematical singularity if it exists in all possible coordinate systems. If there is no physical singularity at a point then the singluarity is purely mathematical and is referred to as a "coordinate singularity."

 

Pete

[ajb]

Pete, (or should I say Wald!) is absolutely correct. A singularity is a loosely defined as a point in which the curvature blows up to infinity. (I have not defined any of this carefully).

 

Singularities in physics are usually viewed as a breakdown of a theory. The standard thing to do in general relativity is to cut them out. Then the presence of a singularity is defined using geodesic completeness, i.e. geodesic don't "fall of the space-time". All this is discussed in Wald.

 

It could be this "cutting out" that Snail is referring to, in this case the singularity is not a point in space-time.

[Royston]

ajb, Pete, thanks for clearing up the confusion. Incidentally, in another thread, ajb recommended Wald's General Relativity, so it's definitely a book I'll be purchasing for future studies.

 

I was referring to the 'cutting out', however I did get in a muddle with my definitions for the singularity Pete was referring to...all valuable information nonetheless, and looking forward to learning more on the subject.

[Pete]

ajb, Pete, thanks for clearing up the confusion. Incidentally, in another thread, ajb recommended Wald's General Relativity, so it's definitely a book I'll be purchasing for future studies.

You're most welcome.

I was referring to the 'cutting out', however I did get in a muddle with my definitions for the singularity Pete was referring to...all valuable information nonetheless, and looking forward to learning more on the subject.

Misner, Thorne and Wheeler define the term singularity in their text Gravitation. I'll post that definition later, perhaps tommorow.

 

Pete

[ajb]

I don't know if there is a completely agreed on definition of a singularity. Intuitively we all know what it means.

 

And please do quote MTW on their definition. I will flick through the GR books I have and see how they define it, rather loosely I expect.

[Pete]

I don't know if there is a completely agreed on definition of a singularity. Intuitively we all know what it means.

 

And please do quote MTW on their definition. I will flick through the GR books I have and see how they define it, rather loosely I expect.

Okey dokey - From Gravitation by Misner, Thorne and Wheeler, page 934

Before examining the theorems on singularities, one must make precise the concept of a singularity. This is not easy, as Geroch (1968) has emphasized in a long treatise i on the wide variety of pathologies that can occur in spacetime manifolds. However, after vigorous efforts by many people, Schmidt (1970) finally produced a definition that appears to be satisfactory. Put in heuristic terms, Schmidt's highly technical definition goes something like this. In a spacetime manifold, consider all spacelike geodesics (paths of "tachyons"), all null geodesics (paths of photons), all timelike geodesics (paths of freely falling observers), and all time like curves with bounded acceleration (paths along which observers are able, in principle, to move). Suppose that one of these curves terminates after the lapse of finite proper length (or finite affine parameter in the null-geodesic case). Suppose, further, that it is impossible to extend the spacetime manifold beyond that termination point-e.g., because of infinite curvature there. Then that termination point, together with all adjacent termination points, is called a "singularity." (What could be more singular than the cessation of existence for the poor tachyon, photon, or observer who moves along the terminated curve?)

 

Pete

[ajb]

I think this definition is the same as "geodesic completeness". Of course it is given very heuristically here.

 

In essence the geodesics "fall off the space-time", i.e. in the above they "terminate". Which is really the same thing. Paths cannot be extended to "infinite time". It is this that is used to signal the presence of a singularity. I am not sure if an "intuitive singularity" is the only thing that can give this "signal". I will have to read Wald and Hawking & Ellis more carefully.

[Pete]

I think this definition is the same as "geodesic completeness". Of course it is given very heuristically here.

I disagree with respect to given very heuristically. Something is called heuristic when it involves or servers as an aid to learning. The definition given by MTW is not of that nature. Perhaps you were expecting something more mathematical? If so then note that the definition given by MTW is defined in terms of mathematical objects. Quite often when something physically basic is defined it can't be given in terms of math since it is that which must be given in order to provide a mathematical description.

In essence the geodesics "fall off the space-time", i.e. in the above they "terminate". Which is really the same thing.

I disagree here too. Falling off the spacetime is different than terminating. Something that terminates has a finite endpoint whereas something that falls off the spacetime might not be as such.

Paths cannot be extended to "infinite time". It is this that is used to signal the presence of a singularity. I am not sure if an "intuitive singularity" is the only thing that can give this "signal". I will have to read Wald and Hawking & Ellis more carefully.

What were you expecting in terms of a definition for it to be rigorous rather than what you call "inuitive"?

 

Pete

[ajb]

The definition we (MTW and I) have given is of course heuristic, in the sense that nothing we have said has been stated mathematically. Nothing said here is at all mathematically rigorously. I don't see why you think it is not. What is true is that all we have said can be made more rigours.

[Pete]

The definition we (MTW and I) have given is of course heuristic, in the sense that nothing we have said has been stated mathematically. Nothing said here is at all mathematically rigorously. I don't see why you think it is not. What is true is that all we have said can be made more rigours.

 

But why do you think that definitions must be mathematical to be rigorous? E.g. define "time" mathematically.

 

Pete

[ajb]

Oh no. You don't understand the ethos of modern theoretical physics.

 

Theoretical physics is a mathematical pursuit. The language needed almost by definition is mathematics. If you don't understand this, why are you reading MTW?

[Pete]

Oh no. You don't understand the ethos of modern theoretical physics.

So you say. But that is no way true.

Theoretical physics is a mathematical pursuit. The language needed almost by definition is mathematics.

To describe physics that is true. But not to define some of the elementary terms.

If you don't understand this, why are you reading MTW?

Just because I disagree with you it in no way means that I don't understand something.

 

Again, please define the terms time and physical space (as opposed to a mathematical space) mathematically or either state that it can't be done or that you know how to.

 

Pete

[ajb]

We are hijacking this thread.

 

I did not mean to be offensive.

 

Lets no do that. I will send you a personal message.

[Pete]

We are hijacking this thread.

 

I did not mean to be offensive.

I know. Sometimes things come out different than one wanted them to. I understand that.

 

Pete

[Mr Skeptic]

We are hijacking this thread.

 

I did not mean to be offensive.

 

Lets no do that. I will send you a personal message.

 

I must say, the disagreements you two (ajb and Pete) have are particularly educational and interesting. I, for one, would not mind seeing more of them.

[ajb]

Disagreements is too strong a work. We just approach some some things from a slightly different perspective sometimes. That's all.