Observing a black hole's singularity

[pywakit]

In classical general relativity the singularity (not quite so easy to define) at the centre of a black hole is a point- infinitesimally small. This is not usually taken to the the "extent" of a black hole. (Again, extent is not so easy to define). The "size" or "extent" is taken to be the Schwarzschild radius (x2 for a diameter etc). For sure it is the Schwarzschild radius that seems to be the interesting thing for the physics.

 

Now, quantum mechanics presumably smears the singularity inside a black hole. This would then regulate the divergence in the curvature/matter density.

 

Yes. Thank you. Do you think a BH with the mass I have described would NOT have physical dimensions? An actual physical object ( spherical if non-rotating, flattened sphere if rotating ) diameter bordered by the Schw. radius?

 

Nice to converse again ajb!

[ajb]

Yes. Thank you. Do you think a BH with the mass I have described would NOT have physical dimensions? An actual physical object ( spherical if non-rotating, flattened sphere if rotating ) diameter bordered by the Schw. radius?

 

I have not been following the thread closely, just your misconception about what people mean by the size of a black hole was clear.

[pywakit]

I have not been following the thread closely, just your misconception about what people mean by the size of a black hole was clear.

 

Language barrier? Could you re-state your comment ajb? I'm not certain I follow.

 

You didn't actually address the question I asked. Defining the size of a BH by the Schw. radius alone does not address the possibility ( if not likelihood ) that a BH containing the mass I hypothesized would have an actual volume.

 

If it did not have actual volume, then we are back, to all intents and purposes, to an infinitismally small point ... or almost equally small 'smear'. And essentially near-infinite density.

 

This would seem to defy reason. It's hard enough to swallow that the mass of a 2 million sol BH would have zero volume. Do you really think the universe's ( space ) physical constraints would allow a BH with a mass of 40,000,000,000,000,000,000,000 sols to have NO volume?

[ajb]

All I meant was there is three different answers to the question of the size of a black hole in the context of the Schwarzschild metric.

 

1) The singularity at the centre is a point. So it is infinity small.

2) The event horizon could also be used to define the size, thus the Schwartzchild radius come into play. This gives a finite size for a finite mass.

3) As the Schwarzchild metric is asymptotically flat we could say that a black hole is infinite in extent. That is we need to be infinitely far away to be in flat space-time.

 

In the context of general relativity there seems to be no bounds on the mass. Again, thinking of the mass as a parameter in the Schwartzchild metric (to avoid worrying about masses more generally) we are free to consider any positive and finite mass. (Positive we maybe able to relax if we are happy to violate classical energy theorems).

 

However, when the Schwarzchild radius becomes comparable to Compton wave length of mass we expect to be outside the domain of applicability of classical general relativity. We expect quantum effects to become important.

 

Similarly, when the curvature of a space-time becomes comparable to Planck length quantum effects must play a role. In fact, the scale at which quantum gravity kicks in could be a lot larger than the Planck length.

 

So it is expected that quantum gravity will stop infinite mass densities.

[pywakit]

All I meant was there is three different answers to the question of the size of a black hole in the context of the Schwarzschild metric.

 

1) The singularity at the centre is a point. So it is infinity small.

2) The event horizon could also be used to define the size, thus the Schwartzchild radius come into play. This gives a finite size for a finite mass.

3) As the Schwarzchild metric is asymptotically flat we could say that a black hole is infinite in extent. That is we need to be infinitely far away to be in flat space-time.

 

In the context of general relativity there seems to be no bounds on the mass. Again, thinking of the mass as a parameter in the Schwartzchild metric (to avoid worrying about masses more generally) we are free to consider any positive and finite mass. (Positive we maybe able to relax if we are happy to violate classical energy theorems).

 

However, when the Schwarzchild radius becomes comparable to Compton wave length of mass we expect to be outside the domain of applicability of classical general relativity. We expect quantum effects to become important.

 

Similarly, when the curvature of a space-time becomes comparable to Planck length quantum effects must play a role. In fact, the scale at which quantum gravity kicks in could be a lot larger than the Planck length.

 

So it is expected that quantum gravity will stop infinite mass densities.

 

Alright. I think I understand. So short answer is ... you are saying a hypothetical BH of this mass will have a physical volume. An actual 3d structure.

 

As far as the gravitational influence ... I think you mean a BH will have a potential for infinite boundries, propogating out from the BH at c.

 

The physical structure can be no larger in diameter than the event horizon. Is this correct?

 

And ( obtuse fellow that I am ) you are also agreeing? that GR allows for a mass this large ( 4^22 SM ).

 

But I am confused by ... " if we are happy to violate classical energy theorems."

 

Would this mass violate those theorems?

 

Lastly, this confused me too ... "However, when the Schwarzchild radius becomes comparable to Compton wave length of mass we expect to be outside the domain of applicability of classical general relativity."

 

Should I enroll in a university?

Edited January 22, 2010 by pywakit

[ajb]

you are saying a hypothetical BH of this mass will have a physical volume. An actual 3d structure.

 

As defined by the event horizon. Thus tends to be what people are talking about by volume or surface area. The surface area of the event horizon seems to be a very important thing in black hole physics and not the volume.

 

As far as the gravitational influence ... I think you mean a BH will have a potential for infinite boundries, propogating out from the BH at c.

 

You would need to be infinity far away in order to be outside the gravitational field, i.e. zero curvature. This is not special to general relativity, the same applies to the Newtonian potential.

 

Now as a Schwarzchild black hole is a particular example of curved space-time you could say that the entire space is the black hole.

 

 

And lastly, the physical structure can be no larger in diameter than the event horizon. Is this correct?

 

The Schwarzchild metric describes the space-time around a delta-function mass. Take a star for example. If we assume it is rotating very slowly then the space-time around the star is described well by the Schwarzchild metric.

 

 

However, the Schwartzchild metric does not describe the space-time inside the star. We do not expect to find "horizons inside stars", but we can think heuristically that the space-time around a star is described by the Schwarzchild metric such that the event horizon lies inside the star.

 

So, the Schwarzchild radius does not give a maximum size in general. It does gives a "purely space-time" structure associated with a point mass , the event horizon.

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And ( obtuse fellow that I am ) you are also agreeing? that GR allows for a mass this large ( 4^22 SM ).

 

General relativity itself does not place constraints on magnitude of the masses. There are questions about how physical such a thing would be, questions related to astrophysics and cosmology. Not directly general relativity.

 

There is also a question of quantum gravity effects, see later.

 

But I am confused by ... " if we are happy to violate classical energy theorems."

 

Would this mass violate those theorems?

 

There are various forms of the classical energy conditions. In essence they say no-one would ever see a negative mass.

 

Lastly, this confused me too ... "However, when the Schwarzchild radius becomes comparable to Compton wave length of mass we expect to be outside the domain of applicability of classical general relativity."

 

Let us think of electrodynamics in particular, on a flat space-time the Compton wavelength of an electron is the distance scale at which effects due to the quantisation of the electromagnetic field must be taken into account.

 

On a curved space-time we need to employ semi-classical gravity, that is quantise the fields in the background of a curved space-time.

 

If the Compton wavelength, which we can think of as the size of the quantum particle is near the scale of the Schwarzchild radius then I would expect a black hole to form.

 

If you solve for the mass, you get the Planck mass. So, we are really outside the scope of classical general relativity. So, any masses near the Planck mass should be viewed as "suspicious" on these grounds.

 

But like I said, using classical general relativity we have no problem. Just that classical relativity is not going to be valid at these scales.

[pywakit]

ajb writes:

 

Now as a Schwarzchild black hole is a particular example of curved space-time you could say that the entire space is the black hole.

 

Thanks ajb. I will think about the rest of your comments for a while before I respond.

 

As for the above, would it not be more technically accurate to say we exist in 'multiple' black holes 'simultaneously' as opposed to one?

[Chriton]

Can a BH still be classed as matter? as far as I have learned, all electrons, then all protons are stripped from the atom, that would just leave the Neutron, so can that still be classed as Matter?