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Author Topic: How can Black Holes Vary in Size?  (Read 9936 times)

Offline Xin

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How can Black Holes Vary in Size?
« on: 21/05/2008 20:58:58 »
Assuming that black holes contain a singularity in its center, I'm confused as to how black holes can vary in size. The singularity is a point of infinite density (and gravity) compressed into zero volume, right? If so, wouldn't that mean that all singularities would technically have to be the exact same "size"? And if they are the same "size", then the sphere of gravitational influence also has to be the same "size"?

It all seems a bit strange to me...wouldn't it make more sense if black holes really weren't "holes", but just incredibly large objects (in terms of mass) that have enough gravity to keep light from escaping? This way we don't have the laws of physics break/fail, and would help explain why black "holes" can be supermassive or extremely tiny enough to be created in a particle accelerator.

Am I way off on this? :)


 

Offline Soul Surfer

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How can Black Holes Vary in Size?
« Reply #1 on: 21/05/2008 23:41:15 »
The gravitational field of a lump of material gets greater as the mass of the material is increased.  the size of the lump depends on the mass and the mean density of the body.  As you approach any gravitating body the gravitational field gradually increases from zero at infinity until you reach the surface of the body or the surface of the event horizon that encloses it if the mass and mean density of the body is great enough.  the event horizon occurs when the escape velocity from the body reaches the velocity of light so not even light may escape from it.

The point at which this happens for black holes depends on the mass.  For a black hole with a mass equal to that of the sun this distance is about one mile.  That is the whole mass of the sun which has a diameter of 864,000 miles has to be compressed into a sphere with a diameter of one mile.

What happens inside a black hole's event horizon is a bit of a mystery but it is almost certainly not a singularity or a point of infinite density.  This is a term used by mathematicians but not physicists.  Physicists know that all gravitating bodies posses some angular momentum which must be conserved and this means that the structure inside must be a circle with a finite size and most probably a toroidal surface like a bagel or polo mint.
 

Offline graham.d

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How can Black Holes Vary in Size?
« Reply #2 on: 22/05/2008 13:55:13 »
It is important to realise that the event horizon of a black hole is only defined as a certain size when viewed from an infinite distance (in practice a reasonably large distance). As you get closer to a black hole and under its gravitational field the apparent event horizon is smaller. The event horizon is the surface from which object cannot escape to infinity. With a sufficiently large black hole you could pass over the theoretical event horizon (that defined as that seen from infinity) as the event horizon you would observe would be smaller. It would have to be a large BH to avoid being torn apart by tidal forces. Of course there would be other problems, not least of which is that you could never escape back to a safe distance.

Rotating BHs are interesting constructs. I seem to remember a paper some years ago that suggested that, as SS says, that rather than a naked singularity there would be a circular structure and that if the BH was big enough, and rotating fast enough, you could (in theory) go through the middle of it.
 

Offline LeeE

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How can Black Holes Vary in Size?
« Reply #3 on: 22/05/2008 16:52:22 »
I think it's still debatable whether a BH consists of a point singularity or a finite sized body, angular momentum notwithstanding.  This is because while it's true for matter, as we know it, to require non-zero size to possess angular momentum, whatever is inside a BH is not matter as we know it.

Because we know that we don't know exactly what is inside a BH, I think it's dangerous to apply an assumption that requires us to know something, to the BH situation where we know that we don't know that something.

Um... I _think_ I've got that right:)
 

Offline Supercryptid

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How can Black Holes Vary in Size?
« Reply #4 on: 22/05/2008 17:22:18 »
I think I've read that Quantum Mechanics prevents objects from having zero size. Therefore, you might expect a black hole's "singularity" to have a size no smaller than the Planck Length instead of zero.
 

Offline syhprum

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How can Black Holes Vary in Size?
« Reply #5 on: 22/05/2008 17:51:42 »
I am at a loss as to why the assumption is made that behind the event horizon matter must have a quasi infinite density, could there not be a further stage of commpression possible past the density of the Neutron star where the star has sunk to a diameter such that it is hidden behind the event horizon.
Protons have a well defined diameter but why can't the constituent quarks not be forced even closer together.
 

Offline graham.d

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How can Black Holes Vary in Size?
« Reply #6 on: 23/05/2008 09:11:37 »
The truth is that we have no idea what state matter is in beyond the event horizon. It is probably a question which has no physical meaning but is rather just an abstract concept. As I said before, you could travel in through an event horizon (the EH as seen from infinity) and could observe that there is no specific change to material in your local environment (providing it was a large enough BH). The question may be akin to saying what was the universe like before the big bang or, to quote an old Zen idea, what is the sound of one hand clapping.
 

Offline lightarrow

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How can Black Holes Vary in Size?
« Reply #7 on: 23/05/2008 13:06:49 »
I am at a loss as to why the assumption is made that behind the event horizon matter must have a quasi infinite density, could there not be a further stage of commpression possible past the density of the Neutron star where the star has sunk to a diameter such that it is hidden behind the event horizon.
Protons have a well defined diameter but why can't the constituent quarks not be forced even closer together.
I also wondered about the same question and I "think" to have understood that the object must keep collassing, whatever kind of counter-forces it finds while doing it; this because space-time curvature is so high that a point object inside it have no other chance than to move towards the singularity (they say the light cones are tilted towards the singularity), so, while time passes, it's the very spacetime curvature that forces the object moving there.
Or something like that...  :)
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #8 on: 23/05/2008 18:41:02 »

Because we know that we don't know exactly what is inside a BH, I think it's dangerous to apply an assumption that requires us to know something, to the BH situation where we know that we don't know that something.


 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #9 on: 23/05/2008 18:48:03 »
...they say the light cones are tilted towards the singularity...

Is that right? Surely, light cones represent the way light (or information) spreads out from a given point. In the case of a BH light is travelling towards a point, not away from it. Light cannot originate from the point, so isn't it a nonsense to talk about lightcones inside an event horizon?
 

Offline LeeE

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How can Black Holes Vary in Size?
« Reply #10 on: 23/05/2008 19:20:47 »
The light cone doesn't so much represent the way that light spreads out from an origin but shows the possible future positions of something.  The current position is always at the apex of the cone, the height of the cone is time and the sides of the cone represent the  lightspeed limit (hence light-cone).  All possible future positions of anything lie within the volume of their light cone.

When a light cone is said to be tilted towards a BH what is happening is that the shape of the light cone is being affected by the BH so that a greater proportion of the possible future positions of the object point towards it.  If the cone intersects the BH EH and the object moves into that region it will captured but if it does not and part of the cone remains outside the EH escape is still theoretically possible.  If the base of the cone is entirely within the EH then no escape is possible because all possible futures point towards the BH.
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #11 on: 23/05/2008 19:34:23 »
I'm aware that the cone represents the possible futures of something, but I was referring specifically to light or information. If you have 2 cones then no light or information can pass between them before they spread enough that they coincide. Until that time, each would be totally unaware of the other's existence.

The full statement I responded to was

Quote
this because space-time curvature is so high that a point object inside it have no other chance than to move towards the singularity (they say the light cones are tilted towards the singularity)

so I was referring to the lightcone of an object inside the EH. Such an object has no options; as Alberto said, "it have no other chance than to move towards the singularity". Therefore the lightcone must collapse to a line terminating at the BH.
 

Offline LeeE

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How can Black Holes Vary in Size?
« Reply #12 on: 23/05/2008 19:47:23 »
Oops - my misunderstanding.

That's an interesting thought re the cone collapsing.  If it could be viewed from outside, the the sides of the cone at the base would have to appear to start contracting inwards and eventually end up as a point (or a quantum object).  At some point in this process it seems to me that the cone could pass through a phase where it appeared broadly symmetrical along the time (height) axis.

 

Offline syhprum

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How can Black Holes Vary in Size?
« Reply #13 on: 23/05/2008 20:33:17 »
Let us imagine we are really in a black Hole, we certainly cannot escape tho we reach 'c' velocity, what do we see about us galaxies and even other black holes.
Would it be any different inside any one of them?.
Could our bursting out from a singularity 13.7 billion years ago really be our time reversed view of our collapse into a black hole.
« Last Edit: 23/05/2008 20:36:13 by syhprum »
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #14 on: 23/05/2008 20:39:23 »
Oops - my misunderstanding.

That's an interesting thought re the cone collapsing.  If it could be viewed from outside, the the sides of the cone at the base would have to appear to start contracting inwards and eventually end up as a point (or a quantum object).  At some point in this process it seems to me that the cone could pass through a phase where it appeared broadly symmetrical along the time (height) axis.


Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #15 on: 23/05/2008 20:42:55 »
Let us imagine we are really in a black Hole, we certainly cannot escape tho we reach 'c' velocity, what do we see about us galaxies and even other black holes.
Would it be any different inside any one of them?.
 

The light would be (infinitely?) blue-shifted, though; so would we actually be able to see anything?

hmmm... I feel another thread creeping up on me.  :D
« Last Edit: 23/05/2008 20:45:45 by DoctorBeaver »
 

Offline graham.d

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How can Black Holes Vary in Size?
« Reply #16 on: 24/05/2008 00:04:47 »
Syphrum, I had a similar thought but then decided it was probably unlikely. What the universe would look like when accelerating towards the centre of a very large black hole and after passing the event horizon is beyond my ability to reason with any certainty and, unfortunately, beyond my ability to calculate within a general relativistic framework - although should be possible by someone with the time and ability. Locally, space will be reasonably normal but I am not sure what the universe would look like on a larger scale. You would be in a gravitational freefall so I am not even sure that distant starlight would be blue shifted. Both your speed and the gravity field will affect the incoming light so I think the actual picture is complex. What role would Lorentz contraction play in what the universe looks like? I can picture these things in Special Relativity (sometimes) but this is strongly within the realm of GR and needs a good deal of maths and subsequent interpretation. It would make a good paper for someone. Any volunteers?
 

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« Reply #17 on: 24/05/2008 12:10:38 »
Quote
You would be in a gravitational freefall so I am not even sure that distant starlight would be blue shifted.

But, surely, photons would gain energy as they approached the EH. Higher energy = shorter wavelength = blue shift, n'est-ce pas?
 

Offline graham.d

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« Reply #18 on: 24/05/2008 15:36:44 »
Yes, and there would be blue shift if you were somehow stopped or slowed by firing huge retro rockets. But if you had free-fallen into the BH you would have a huge velocity and moving away from the stars behind you so there would be a large doppler redshift which (I think) would exactly nullify the gravitational blue shift.
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #19 on: 24/05/2008 15:45:05 »
Yes, and there would be blue shift if you were somehow stopped or slowed by firing huge retro rockets. But if you had free-fallen into the BH you would have a huge velocity and moving away from the stars behind you so there would be a large doppler redshift which (I think) would exactly nullify the gravitational blue shift.

I shall have to ponder on that a bit more.
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #20 on: 24/05/2008 15:59:16 »
Update on my pondering.

Light cannot escape from an EH, so the escape velocity is >c. But if an object free-falls across an EH, what is its velocity? I don't see that it necessarily has to be relativistic (That would be especially true of supermassive BHs).

What if the object were approaching the EH at an angle? Wouldn't the angle of approach have some bearing on how fast it was receding from distant objects and, hence, the resultant red shift (objects at 90o would hardly have any red shift)?

And that makes me ponder a different aspect of the question. If you approached the EH at an angle, wouldn't the light from behind you be shifted differently from that ahead of you?

Actually, that would be the case no matter what your angle of approach; objects at 90o would have no shift either way.

Sorry if my thoughts are a bit haphazard, that's just the way I think about things.
 

Offline LeeE

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How can Black Holes Vary in Size?
« Reply #21 on: 24/05/2008 17:40:51 »
Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.

Sort of - because the cone would be in a gradient, the base would have to contract towards a point as it approached the singularity but I would imagine the sides of the cone to be smoothly curved and it would end up as a sort of elongated egg-shape, but with pointed ends instead of rounded ones.

There wouldn't be true symmetry along the time axis, of course, because the axis is directional, but the shape of the cone would approach symmetry along that axis.  All I think it actually signifies is that in such a situation there's only one possible future, which we know already:)  It does seem like quite a nice way to illustrate it though.
 

Offline DoctorBeaver

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How can Black Holes Vary in Size?
« Reply #22 on: 24/05/2008 17:58:10 »
Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.

Sort of - because the cone would be in a gradient, the base would have to contract towards a point as it approached the singularity but I would imagine the sides of the cone to be smoothly curved and it would end up as a sort of elongated egg-shape, but with pointed ends instead of rounded ones.


A fat, pointy-ended sausage!  :D

Quote
All I think it actually signifies is that in such a situation there's only one possible future, which we know already

Indeed. Until the entire base of the cone intersects the EH, all possible futures are still options. But when it does - SCHLOOOOOP!

heh - can we say that the diminishing fatness of the sausage depends on the schloooopiness of the BH? Imagine presenting that in a paper! :D
« Last Edit: 24/05/2008 18:02:06 by DoctorBeaver »
 

Offline graham.d

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How can Black Holes Vary in Size?
« Reply #23 on: 24/05/2008 18:55:26 »

Light cannot escape from an EH, so the escape velocity is >c. But if an object free-falls across an EH, what is its velocity? I don't see that it necessarily has to be relativistic (That would be especially true of supermassive BHs).


If you fell in from a long way off it would be relativistic. The definition of the event horizon is the surface from which the escape velocity equals the speed of light - ergo, if falling from an infinite distance (by symmetry) you would just achieve this speed at the EH. This is not allowed by special relativity but it means that the universe would have Lorentz contracted in your direction of travel considerably and the BH's mass would be even higher relative to you. There was a paper some years ago which showed what objects would look like if you were passing them at relativistic speeds; the results were not what you would expect intuitively, and this was just Special Relativity. As I said before, this needs a lot of maths work to glean insight.
 

Offline LeeE

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How can Black Holes Vary in Size?
« Reply #24 on: 24/05/2008 19:01:27 »
I think that using escape velocities might actually be confusing the issue here.

An escape velocity is the initial speed that when imparted to an object is sufficient to overcome an opposite acceleration due to gravity so that it will end up infinitely far away, with infinitely small speed.

In the case of a BH, the EH marks the point along the gravity gradient from the BH where the escape velocity from the BH is equal to c, so nothing within an EH can escape it by being given a sufficient initial velocity, because nothing can be imparted with a speed > c.

However, this doesn't mean that anything located at the EH, or even within it, has to be travelling at c.  For example, on the surface of the Earth, the escape velocity is about 11200 m/s but none of us actually on the surface of the Earth is travelling at that speed, so you wouldn't necessarily need to be travelling at c when you cross the EH and you should be able to still see the universe outside.  The light falling into the BH will be blue-shifted but as you accelerate towards the singularity the light will appear to be more and more red-shifted until you reach the point where your velocity approaches c and the apparent energy of the light reaching you approaches zero.
 

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How can Black Holes Vary in Size?
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