# How fast can a black hole grow (when it first forms)?

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#### evan_au

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##### How fast can a black hole grow (when it first forms)?
« on: 17/12/2012 10:38:09 »
When a black hole first forms (eg via gravitational collapse of a star), how quickly does the event horizon expand?

In particular, if the density of a region is just short of the critical density that would form a black hole, could the event horizon (temporarily) expand outwards at greater than the speed of light?

#### imatfaal

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #1 on: 17/12/2012 18:13:31 »
Have to think about that one Evan.  One thing to bear in mind is that the event horizon is non-physical and does not allow transmission of information (apart from the fact that one is about to be horribly torn apart by tidal forces) - so why should it not.

I am not sure it can be done heuristically - you might have to imagine a hot neutron star density sort of thingie, with the central density just below critical and being kept there by outward pressure of internal heating.  Shut off the heating, centre will contract ...and do some horrid maths.

Off the top of my head I would say that if enough of the off-centre region was close enough to the critical density to collapse quickly after the initial central collapse, then it would already have collapsed due to mutual gravitational attraction
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#### Ethos_

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #2 on: 20/12/2012 21:39:55 »
When a black hole first forms (eg via gravitational collapse of a star), how quickly does the event horizon expand?
Let's remember that the event horizon is a function of the gravitational mass of the body. And shortly before collapse, the body has already attained sufficient mass at it's surface to make escape only possible by reaching velocity very close to light speed anyway. In effect, when collapse occurs, the event horizon will propagate very close to the last spherical radius of the initial mass. In reality, the event horizon doesn't really expand. It just takes place very close to where the surface of the original mass last stood.
"The more things change, the more they remain the same."

#### JP

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #3 on: 20/12/2012 22:31:28 »
When a black hole first forms (eg via gravitational collapse of a star), how quickly does the event horizon expand?
Let's remember that the event horizon is a function of the gravitational mass of the body. And shortly before collapse, the body has already attained sufficient mass at it's surface to make escape only possible by reaching velocity very close to light speed anyway. In effect, when collapse occurs, the event horizon will propagate very close to the last spherical radius of the initial mass. In reality, the event horizon doesn't really expand. It just takes place very close to where the surface of the original mass last stood.

Indeed.  For someone far away from the star, they wouldn't feel any difference in gravity between an uncollapsed star and the collapsed black hole, assuming the simple model of a uniform, spherical, nonrotating star.  At the event horizon, gravity just keeps getting stronger as the star collapses until light can't escape.  For a rotating black hole, I don't know what the collapse is like.

#### CliffordK

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #4 on: 21/12/2012 00:44:49 »
Hmmm

The event horizon is defined as the point where the escape velocity = c

c = $$\sqrt{\frac{2GM}{r}}$$

where c is the speed of light, 300 million m/s
G is the gravitational constant, 6.67×10−11 $$\frac{m^3}{kg s^2}$$
M is the mass of the black hole.

I think r has to be the distance to the event horizon.

So, if the mass below the event horizon is symmetrically distributed, and more or less unchanging, then the event horizon should also be unchanging, independent of density.

Now, if the black hole is formed during a supernova.  Then could one have an expanding cloud of debris that would be outside of the event horizon, which could then start to rapidly contract?

Another possibility for the formation of a black hole might be the collision of 2 neutron stars, in which as it forms, part of the stars might be within the event horizon, and part of them might be outside of the event horizon.  Or, the same thing might be true with the collision of 2 black holes, or a star with a small black hole.

Of course, I also mentioned symmetrically distributed mass.  With astronomical events, that may not always be the case.

#### Ethos_

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #5 on: 21/12/2012 01:41:44 »

Now, if the black hole is formed during a supernova.  Then could one have an expanding cloud of debris that would be outside of the event horizon, which could then start to rapidly contract?
Absolutely my friend........Your observations are correct and leads one to believe that it is more likely that; Either the event horizon stays fairly close to the original radius in the case of a moderate event or, in the case of a violent occurrence, the event horizon would most likely shrink due to loss of captured mass.
"The more things change, the more they remain the same."

#### imatfaal

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #6 on: 21/12/2012 17:05:42 »

Now, if the black hole is formed during a supernova.  Then could one have an expanding cloud of debris that would be outside of the event horizon, which could then start to rapidly contract?
Absolutely my friend........Your observations are correct and leads one to believe that it is more likely that; Either the event horizon stays fairly close to the original radius in the case of a moderate event or, in the case of a violent occurrence, the event horizon would most likely shrink due to loss of captured mass.

Ethos - I think you are assuming that Evan was asking about the event horizon as a purely external "manifestation" - but that is only its final position.   Stars collapse from the inside to the outside - not all at once; at least I think they do :-)   The first volume that has compression high enough to go past the various degenerate states is in the centre - where most of the other mass is "falling down" onto it.  The matter which does not have the velocity to stay out continues to fall in - it is no longer supported by the superdense centre.  Some matter ends up ejected, other stuff is lost to the blackhole; but I do not believe that the actual process of collapse is instantaneous.  You go from a situation where you have a star to a blackhole with a much much smaller radius than the star - but at some point there was a start of blackhole which progressed to the final blackhole.  How I interpreted Evan's question was - how fast does this transition move
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#### Ethos_

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #7 on: 21/12/2012 17:54:54 »

How I interpreted Evan's question was - how fast does this transition move
Fair observation imatfaal, I may have misinterpreted his question. In respect to the question raised; How fast does this transition takes place? I'm not sure we can answer this. One might think that because the velocity of light is the threshold between this massive star and the singularity, this transition might advance at that velocity. This would be my position, however, we have no empirical evidence to support this notion. Someone here with a better background in the math behind the physics may speculate on this possibility.
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#### yor_on

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #8 on: 22/12/2012 06:43:05 »
It's a weird one indeed Ethos

And I also think that 'c'  should regulate the change into a singularity, but after that the field is wide open for speculation. It depend on whether you expect the inside of a black hole to obey our physics I guess, or not?
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#### evan_au

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #9 on: 22/12/2012 09:43:53 »
I am guessing that within a star that has exhausted its fuel, the density will be highest at the center. When this density reaches a critical value,  a black hole will form within the star. http://en.wikipedia.org/wiki/Chandrasekhar_limit#Applications

Does the event horizon just "appear", or does it expand out from the denser central core?

(I expect that as the remainder of the star collapses into the black hole, the event horizon will increase a bit more: Black hole Mass M increases, so radius r will also increase.)

#### Ethos_

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #10 on: 22/12/2012 15:17:02 »
Does the event horizon just "appear", or does it expand out from the denser central core?
The radius at which escape velocity becomes the speed of light and determines the sphere of all events which can no longer be observed from outside. We call this the Event Horizon. And this sphere is determined by the total mass of the body relative to it's volume. And this total mass/volume, when calculated, is called the packing fraction. If the body is undergoing a supernova type explosion, then the total mass/volume will vary greatly over time until gravity is given opportunity to reassemble all local matter. In any case, the escape velocity of a body that reaches the speed of light is what we refer to as the event horizon. So where and how fast this radius occurs depends entirely upon the aggregate mass and energies of compression. I tend to think this final stage occurs at light speed because light speed is the threshold for these criterion.

Black holes can form either thru gravitational attractions or thru external compressions. I think the easiest way to examine this question is to look at the least violent example of black hole formation. Let's start with a neutron star, or as some theories have suggested, a quark star. These bodies are rather stable and from this starting point we can add matter a little at a time until we reach a point where just one more small volume of matter initiates collapse. Interestingly enough, I feel that this point of mass/volume is a physical constant that we have yet to acknowledge. I'm familiar with the Schwarzchild solution; r=2Gm/c^2 but this is not the physical constant I'm referring to. This formula is only a relationship between constants. The constant I'm speaking about is: What number of neutrons, or total mass, when assembled together in empty space without perturbation or external energies of compression  will initiate collapse?

When done thru this method, the event horizon will establish it's self where the surface of the former body existed. Now comes the 64 thousand dollar question. How fast will the former body shrink to the singularity leaving the event horizon where the former surface last stood? I have no proof but I believe that this event occurs at light speed.
« Last Edit: 22/12/2012 18:59:59 by Ethos_ »
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#### imatfaal

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #11 on: 24/12/2012 12:41:53 »
Does the event horizon just "appear", or does it expand out from the denser central core?
The radius at which escape velocity becomes the speed of light and determines the sphere of all events which can no longer be observed from outside. We call this the Event Horizon.
You have to be slightly careful with escape velocities.  Back to earth for an example; you do not need to have a velocity of 11.2km/s to escape earth's gravity if you are powered!  If you maintain any speed away from the earth you will eventually leave - but the escape velocity is the unpowered speed that is necessary for you to escape whilst coasting with no additional force.  Whilst the event horizon of a black hole is the boundary at which the escape velocity would be the speed of light - it is better thought of as a region where all paths are so curved that they lead back into the blackhole; even lightlike paths are so warped that no exit is possible, and as the forward paths of matter are constrained to be less movement in space than lightlike then matter cannot escape.

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And this sphere is determined by the total mass of the body relative to it's volume. And this total mass/volume, when calculated, is called the packing fraction.
The radius of the sphere/horizon depends on the mass.  the mass/volume aka density of the sphere formed by the event horizon at the Schild radius can vary hugely - the mass (if uncompressible) of a sphere of matter grows with the third power of the radius ; thus eventually even water etc in a great enough quantity would have a Schild radius external to its physical radius - and be a blackhole with an event horizon.

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If the body is undergoing a supernova type explosion, then the total mass/volume will vary greatly over time until gravity is given opportunity to reassemble all local matter. In any case, the escape velocity of a body that reaches the speed of light is what we refer to as the event horizon. So where and how fast this radius occurs depends entirely upon the aggregate mass and energies of compression. I tend to think this final stage occurs at light speed because light speed is the threshold for these criterion.

Black holes can form either thru gravitational attractions or thru external compressions. I think the easiest way to examine this question is to look at the least violent example of black hole formation. Let's start with a neutron star, or as some theories have suggested, a quark star. These bodies are rather stable and from this starting point we can add matter a little at a time until we reach a point where just one more small volume of matter initiates collapse. Interestingly enough, I feel that this point of mass/volume is a physical constant that we have yet to acknowledge. I'm familiar with the Schwarzchild solution; r=2Gm/c^2 but this is not the physical constant I'm referring to. This formula is only a relationship between constants. The constant I'm speaking about is: What number of neutrons, or total mass, when assembled together in empty space without perturbation or external energies of compression  will initiate collapse?
Not sure what you mean by your description of the Schild solution to EFE - it has two variables mass and radius, and like most equations it explains what happens to one when you vary the other.  The problem with your follow up question is that there is never an un-perturbed build up of fermions - they fight to remain apart, and nothing is ever truly at rest - remember that neutron stars and the odder form of degenerate matter are predictions of quantum mechanics so ZPE are important.  But in theory any density can form a blackhole (ie Schild radius external to physical radius) - in practical terms you need heavy stuff.

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When done thru this method, the event horizon will establish it's self where the surface of the former body existed. Now comes the 64 thousand dollar question. How fast will the former body shrink to the singularity leaving the event horizon where the former surface last stood? I have no proof but I believe that this event occurs at light speed.
Yes that's a nice way of looking at it.  And the internal stuff - Agree no way but speculation.
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

#### Ethos_

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##### Re: How fast can a black hole grow (when it first forms)?
« Reply #12 on: 24/12/2012 16:49:56 »
Yes that's a nice way of looking at it.  And the internal stuff - Agree no way but speculation.
Thanks my friend for your excellent comments, your attention to these questions is much appreciated. And of course, my reference to the escape velocity relative to the Child radius is much over simplified. And concerning these uncertainties, we have Heisenberg as a testimony. One could say: The only thing that is certain is uncertainty. This is especially true at the quantum level but becomes less a problem at the macro.

Now looking at the macro level: My question is about feeding this neutron star until collapse is initiated. My point here is, leaving out all possible external influence, there remains a point at which gravity will overcome this assemblage of neutrons resulting in collapse. And this total mass number is of come coincidence. If you would have an interest, I'll explain later.

We all realize that no experiment is without variance and for this reason, repeatability is the foundation of the scientific method. Regretfully, in the case of this thought experiment, we are not able to test even once. Therefore, our best guess is truly only speculation.

Thanks again my friend for your thoughts. I find that many times, members that respond to topics often don't take the time to read the entirety of the post. You have proven to me that you are honest enough to give these thoughts just consideration.
"The more things change, the more they remain the same."