Black Hole

[untier]

Will a black hole be infinitely small while it's absorbing more and more materials, since every particle includes an infinitely small universe internally?

[ajb]

Will a black hole be infinitely small while it's absorbing more and more materials...

 

In the context of general relativity the singularity inside a black hole is a point. It will continue to be a point as test particles fall in.

 

However, no-one really expects such a singularity to exists in nature. Quantum effects presumably regulate the singularity.

 

... since every particle includes an infinitely small universe internally?

 

Pardon?

[untier]

 

 

 

Pardon?

 

 

I mean inside a particle, such as an atom, there is a system and the system has many functional particles. Inside each of these particles there is a system and the system includes many functional particles as well, and so forth. This situation seems infinite and you can always get infinitely small things out of it, thus it seems like there's an infinitely small universe in it.

 

If a black hole must have a shape and volume, every time it eats enough material and collapses again the material and structure of it will be reformed stronger in order to sustain extremely more gravity?

Edited March 6, 2010 by untier

[KennyC]

I don't think there is any evidence to support your "turtles all the way down" hypothesis.

[ajb]

I mean inside a particle, such as an atom, there is a system and the system has many functional particles. Inside each of these particles there is a system and the system includes many functional particles as well, and so forth. This situation seems infinite and you can always get infinitely small things out of it, thus it seems like there's an infinitely small universe in it.

 

An atom consists of a nucleus and electrons.

 

The nucleus consists on protons and neutrons which themselves consists of quarks.

 

As far as the experimental evidence goes electron and quarks are fundamental. That is there appears no internal structure to them. This is in agreement with the standard model of particle physics.

 

However, it is not thought that the standard model is the final word on particles and forces. It may be the case that the fundamental particles are different vibrational modes of fundamental strings. Or there maybe internal structure that is beyond our current experimental range.

 

Anyway, it is not believed that one can keep on forever dividing up matter.

 

 

If a black hole must have a shape and volume, every time it eats enough material and collapses again the material and structure of it will be reformed stronger in order to sustain extremely more gravity?

 

I don't know what you mean by collapse again.

 

If you feed a black hole the volume (or more importantly it turns out) of the event horizon increases.

[untier]

 

I don't know what you mean by collapse again.

 

If you feed a black hole the volume (or more importantly it turns out) of the event horizon increases.

 

i mean while the mass of the black hole increases, the gravity of it is increasing. So won't there be a limit extent that according to the cube-sqare law again the black hole itself can't bear its own inward force? Then won't the molecules or even atoms of it be broken? What will happen next? Won't a new stronger material be born against that overwhelming pressure to get to a new balance?

[ajb]

The black hole should be thought of as a point of infinite curvature hidden behind a horizon, a bit like a one way mirror. Things fall in but never escape.

 

One way to quantify how "strong" a black hole is to examine the surface gravity as defined at the horizon. (It is a more complicated in general, but not to worry)

 

For a non-rotating non-charged black hole we have

 

[math]\kappa = \frac{1}{4M}[/math]

 

where [math]M[/math] is the mass of the black hole.

 

Is there a limit to the mass of a black hole? There is no limit built into general relativity that I am aware of. Any limit to observed black hole masses is presumably "astrophysical" in nature.

[KennyC]

But wait doesn't the whole concept of mass break down inside a black hole? Maybe the size (diameter?) of the event horizon world correspond to the previous mass consumed?

[Radical Edward]

 

Is there a limit to the mass of a black hole? There is no limit built into general relativity that I am aware of. Any limit to observed black hole masses is presumably "astrophysical" in nature.

 

There is a low mass limit - it is roughly the planck mass. The actual limit is such that the reduced Compton Wavelength (which is the minimum size of the region at which a mass of M can be localised) exceeds half of the Schwarzschild radius. below this mass, there is no physical description of black holes.

[ajb]

But wait doesn't the whole concept of mass break down inside a black hole? Maybe the size (diameter?) of the event horizon world correspond to the previous mass consumed?

 

Well, the mass of a black hole is well defined.

 

There are three commonly used notions of mass

1) Bondi,

2) ADM,

3) Komar.

 

For the Schwarzchild metric these all agree.

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There is a low mass limit - it is roughly the planck mass. The actual limit is such that the reduced Compton Wavelength (which is the minimum size of the region at which a mass of M can be localised) exceeds half of the Schwarzschild radius. below this mass, there is no physical description of black holes.

 

As you have said, you can put the Compton wavelength equal to the Schwarzchild radius and you get the Planck mass.

 

So this gives you a "maximum mass of a particle before it becomes a black hole". A particle with mass less than this will not form a black hole.

 

That said, as quantum gravity should be important at this scale it is difficult to see if this mass can really be interpreted in this way.

[KennyC]

Well, the mass of a black hole is well defined.

 

There are three commonly used notions of mass

1) Bondi,

2) ADM,

3) Komar.

 

For the Schwarzchild metric these all agree.

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Consecutive posts merged

 

..

 

I'm still not sure what that says. Does the Schwarzchild radius vary depending on the "size"/mass of the black hole?

 

Okay, I looked it up on Wikipedia.....got it. Thanks.

[Radical Edward]

Well, the mass of a black hole is well defined.

 

There are three commonly used notions of mass

1) Bondi,

2) ADM,

3) Komar.

 

For the Schwarzchild metric these all agree.

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Merged post follows:

Consecutive posts merged

 

 

As you have said, you can put the Compton wavelength equal to the Schwarzchild radius and you get the Planck mass.

 

So this gives you a "maximum mass of a particle before it becomes a black hole". A particle with mass less than this will not form a black hole.

 

That said, as quantum gravity should be important at this scale it is difficult to see if this mass can really be interpreted in this way.

 

well it is the minimum mass that a black hole can be. any masses of this size or larger would have to be of sufficient density. As you say though. quantum gravitational effects would most likely be important on this sort of scale anyway, so it could be way out. Also if there are higher spatial dimensions that are bigger than a planck length, it would also be different. I'm just working with what we have to go on at the moment though - I don't want to drag things like string theory and quantum loop gravity in here because they are so speculative.

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But wait doesn't the whole concept of mass break down inside a black hole? Maybe the size (diameter?) of the event horizon world correspond to the previous mass consumed?

 

not really. Black holes are defined by their mass, their charge and their angular momentum. The diameter is exactly related to the mass - this is the equation:

 

[KennyC]

....

 

not really. Black holes are defined by their mass, their charge and their angular momentum. The diameter is exactly related to the mass - this is the equation:

 

 

Yep, thanks, looked it up, but I appreciate it.

[ajb]

Black holes are defined by their mass, their charge and their angular momentum.

 

This is the no-hair theorem. It holds in 4-d.

 

There are counter examples in higher dimensions with non-minimally coupled scalar fields for example.

 

And what I said about a maximum mass particle before it becomes a black hole is the same as your claim that it is a minimum mass of a black hole. (At least to orders of magnitude and not worrying about quantum gravity etc.) Wikipeda calls such a particle of Planck mass a Planck particle, it would be a tiny black hole.

Edited March 7, 2010 by ajb

[Quetzalcoatl]

Reading this thread made me wonder:

The curvature of space-time is strongly related to energy density. Now a photon has [math]E=h\upsilon[/math]. Thinking of the wavelength as the "diameter" of the photon, [math]{\lambda}=\frac{c}{\upsilon}[/math] and so, assuming the following:

 

[math]

\left\{ \begin{gathered}

E=h\upsilon \hfill \\

M_{eff}=\frac{E}{c^{2}} \hfill \\

r_{s}=\frac{2GM_{eff}}{c^{2}} \hfill \\

2r_{s}=\lambda \hfill \\

\end{gathered} \right.

[/math]

 

After some manipulating we get:

[math]\upsilon=c^{2}\sqrt{\frac{c}{4Gh}}[/math]

 

1. Above this, would a black hole form instead of a photon? Would this put an upper limit on an EM wave's frequency?

2. What about a doppler shift? Would that turn a photon into a blackhole?

3. Would two smaller photons crossing paths turn into one blackhole?

 

Been nice practicing some LaTex too...

[Radical Edward]

nice answer here:

 

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970412e.html

[Quetzalcoatl]

Thanks, I was wondering what observations have yielded. They say frequencies around [math]10^{27}[Hz][/math] have been detected. My little calculation gives frequencies much higher ([math]3.7\times10^{42}[Hz][/math] to be more exact). I'm not sure it is possible to find this kinda stuff in nature. Packing [math]2.5\times10^{9}[Joules][/math] in one photon sounds extreme to say the least.