How many dimensions are there in a black hole

[vinayjain]

So - do you mean to suggest that a BH increases it's mass at a finite rate only from the pov of an observer following the mass?

We would not expect to measure the mass of a black-hole from the pov of something falling into it would we? Surely we'd stand back and observe the schwarzchild radius (somehow) as mass falls into the BH. (Otherwise, how do we get the data back to the lab?)

So, such an observer measuring the radius against time would see what?

If it takes an infinity of the observers time for the BH to increase it's mass, surely the graph of radius against time will be flat?

Note: these are pedagogical guiding questions.

There has been a part-answer already: what happens to the schwarzchild radius as the matter approaches it? Still, what sort of time scale are we talking about?

size of the event horizon will be define the size of a black hole

 

[vinayjain]

When you compress a body, you are putting energy into it. This raises particles to higher energy states. In an attempt to reach equilibrium (ground state), the matter will shed energy in the form of light and heat.

(This is, of course, a simplified explanation)

actually what i understand by compressing a gas is that a force need to be applied from every aspect in order to fit the volume in a smaller place.....so we get a gravitational force which is appied to the gases from black hole so the simple mechanism would be it should move inside the event horison so i want to ask is this how does gases gets compressed in accretion disk when there is no other force is applied other than the black hole?

Sorry if my question or understanding sense stupid as I am not a physics guy

 

[mkarger]

The forces inside the disk are complex as both the gravitational pull of the black hole and the gravitational pull of the matter act on the body.

But, you can push on one side and effect the pressure throughout an entire body as there is a resistance to flow. It's a ripple effect.

 

[Simon Bridge]

size of the event horizon will be define the size of a black hole

While correct, does not actually answer the question.

Come on folks - someone is sitting a safe distance from a black hole that is receiving mass at a steady rate (maybe he is chucking rocks at it?) and is plotting it's mass against time - as measured by his stopwatch. What shape is the plot?

 

[vinayjain]

While correct, does not actually answer the question.

Come on folks - someone is sitting a safe distance from a black hole that is receiving mass at a steady rate (maybe he is chucking rocks at it?) and is plotting it's mass against time - as measured by his stopwatch. What shape is the plot?

as usual as time passess and he is still chucking stone at black hole mass of the black hole will increase

 

[vinayjain]

what will happen to a black hole if it goes on pulling things inside for its lifetime and become a supermassive black hole...will it going to become a quasar or not ?

 

[Drakkith]

what will happen to a black hole if it goes on pulling things inside for its lifetime and become a supermassive black hole...will it going to become a quasar or not ?

IF there is infalling material and it emits large amounts of radiation in jets, then yes. If not, then no. The black hole in the center of the milky way is not a quasar, yet it is a supermassive black hole. Interactions may throw large amount of matter into later on and turn it into a quasar again, but there's no way to know now.

 

[Simon Bridge]

A supermassive black hole is somewhat different to a stellar black hole.
The radiation from the quasar comes from the accretion disc.

I've been trying to work out if a supermassive BH must collapse under it's own gravity - modelling one as gas in a box say, no energy gets out (correct for Hawking radiation perhaps). Someone must have done this - pointers?

 

[Drakkith]

A supermassive black hole is somewhat different to a stellar black hole.
The radiation from the quasar comes from the accretion disc.

I've been trying to work out if a supermassive BH must collapse under it's own gravity - modelling one as gas in a box say, no energy gets out (correct for Hawking radiation perhaps). Someone must have done this - pointers?

I don't understand, a black hole has already collapsed, so what exactly are you asking? Also, a supermassive black hole is exactly like a stellar one except for having more mass correct?

 

[Simon Bridge]

Work it out - Schwartzchild radius increases with mass, but the radius (fixed density) increases with the cube-root of mass ... so you don't have to have collapse for the schwartzchild radius to exceed the radius of our hypothetical ball of stuff.

At water density, you get a BH at 150,000,000 solar masses.

But to stay like that, it needs a reason to not collapse completely under it's own gravity.
A star will do this eventually because it runs out of energy, but for a SMBH energy is not getting past the event horizon and gravity decreases as you approach the center.

Of course, uniform density is quite a big ask.

 

[Drakkith]

A supermassive black hole has already collapsed. Otherwise it couldn't have a Schwartzchild radius as the matter would be spread out far too much. Consider a nuetron star. It currently does not have a Schwartzchild radius that can be reached, however if we compressed it further it the matter falls within the Schwartzchild radius and it becomes a black hole. But to do that it must collapse. As far as I know you are referring to something akin to an extremely massive star, however I don't think they can get anywhere near the mass of a supermassive black hole without blowing themselves apart before they ever collapse.

 

[Simon Bridge]

I'm sorry, the math contradicts you. A uniform density ball of water density matter will have a Schwarzschild radius greater than it's physical extent so it is clearly not "spread out far too much".

http://iopscience.iop.org/0264-9381/16/12A/301/
... behind a paywall, discusses supermassive black holes with water density.

Usually it is assumed that the mass has already collapsed though one can easily imagine a 150,000,000 solar mass diffuse cloud of gas contracting under it's own gravity becoming dense enough (water - remember) to form a supermassive black-hole without blowing apart. Why would it? Probably won't be homogeneous though... so local contractions could ignite etc. In practise, this would be something that would be part of a much bigger cloud as in the middle of a galaxy as it is forming - which messes the math. Still...

I have to be careful with the metric inside the BH that is formed, but I am suggesting that, Hawking radiation notwithstanding, a hydrostatic equilibrium may exist inside the schwarzchild radius which may be self-perpetuating. It my be that the changed metric will prevent it.

http://iopscience.iop.org/0004-637X/703/2/1257/pdf/0004-637X_703_2_1257.pdf
... empirically examines hydrostatic equilibrium constraints on SMBHs - it appears that SMBH may form from gas that is at or near equilibrium.

I cannot be the first to consider this, and the idea is compelling enough that even if it is totally wrong, we'll only need to deal with it again later.

 

[Drakkith]

I'm sorry, the math contradicts you. A uniform density ball of water density matter will have a Schwarzschild radius greater than it's physical extent so it is clearly not "spread out far too much".

Except that it would collapse to form a black hole. We cannot ignore the fact that the matter cannot hold itself up against gravity indefinitely. Any REAL object will never have a Schwarzschild radius larger than itself and avoid becoming a black hole.

Usually it is assumed that the mass has already collapsed though one can easily imagine a 150,000,000 solar mass diffuse cloud of gas contracting under it's own gravity becoming dense enough (water - remember) to form a supermassive black-hole without blowing apart. Why would it? Probably won't be homogeneous though... so local contractions could ignite etc. In practise, this would be something that would be part of a much bigger cloud as in the middle of a galaxy as it is forming - which messes the math. Still...

One cannot easily imagine this happening because it is impossible. Collapsing gas clouds generate stars and tremendous energy from gravitational collapse.

http://iopscience.iop.org/0004-637X/703/2/1257/pdf/0004-637X_703_2_1257.pdf
... empirically examines hydrostatic equilibrium constraints on SMBHs - it appears that SMBH may form from gas that is at or near equilibrium.

The paper is referring to the surrounding interstellar medium well after the black hole has formed. If the interstellar medium is in hydrostatic equilibrium it is possible to accurately measure the mass of the black hole from it. An object cannot have a Schwarzschild radius larger than itself, otherwise it is a black hole and has collapsed.

 

[vinayjain]

schwarschild radius is the radius of a massive object at which it can become a black hole...like for sun it means that if whole mass of the sun will be condensed in the radius of 3 kM it will become a black hole which means that schwarschild radius only exists when an object collapsed in itself to form a black hole....it does not exists in an uncollapsed object...

 

[Simon Bridge]

Any REAL object will never have a Schwarzschild radius larger than itself and avoid becoming a black hole.

I have not suggested otherwise. An object whose Schwarzschild radius is bigger than itself is, by definition, a black hole. I wonder if we are talking past each other?

The paper is referring to the surrounding interstellar medium well after the black hole has formed.

I know. How much material are they talking about?

Collapsing gas clouds generate stars and tremendous energy from gravitational collapse.

Normally yes. But it does not have to happen - if low(er) temp coolants are in low concentration (eg. early universe) then a gas cloud on the scale I'm talking about could contract isothermally at the order of 10^4K (virial) into a halo - with no sub-fragmentation ... eg. no star formation. Fragmentation could also be suppressed through inflow turbulence right?

We cannot ignore the fact that the matter cannot hold itself up against gravity indefinitely.

Seriously? So you think that planets and neutron stars will eventually collapse against their own gravity to form black holes? Perhaps you'd like to qualify that statement?

Stars can balance their gravitational collapse via thermo-nuclear reactions. They only collapse in the end because they run out of fuel and radiate away their heat. But, inside the event horizon, the heat cannot escape. If an event horizon forms before the stars ignite, would the system ever run down?

The math says that low density objects can become black holes.
There are mechanisms that allow low density objects to balance their gravitational collapse.

So - how is it "impossible" for this to happen?

FWIW: I do realize that there are models for the formation of SMBHs which start out with stellar "seed" BHs and collapsing star clusters rather than the non-fragmenting gas-cloud collapse I've been going on about. afaik: these are competing, possibly complimentary, ideas and neither model has been definitively ruled out.

In fact, star formation is a major bottleneck in the stellar seed formation, which could be overcome by including direct collapse elements on a smaller scale.

Normally such a large mass could never find a mechanism to balance it's gravity - however, normally a big star would have exhausted it's internal energy supplies by radiation before it can collapse past it's Schwarzschild radius. In the case of the masses under consideration, it is likely that this will happen before energy sources are gone - so what happens to that energy?

 

[Drakkith]

I know. How much material are they talking about?

What?

Normally yes. But it does not have to happen - if low(er) temp coolants are in low concentration (eg. early universe) then a gas cloud on the scale I'm talking about could contract isothermally at the order of 10^4K (virial) into a halo - with no sub-fragmentation ... eg. no star formation. Fragmentation could also be suppressed through inflow turbulence right?

I have no idea what you're talking about. Lower temp coolants?

Seriously? So you think that planets and neutron stars will eventually collapse against their own gravity to form black holes? Perhaps you'd like to qualify that statement?

I cannot see how you came to the conclusion that I was talking about planets and such.

Stars can balance their gravitational collapse via thermo-nuclear reactions. They only collapse in the end because they run out of fuel and radiate away their heat. But, inside the event horizon, the heat cannot escape. If an event horizon forms before the stars ignite, would the system ever run down?

There would never be a system in the first place. Consider a neutron star that absorbs material from a nearby star. Eventually the mass of the neutron star is so great that it collapses to form a black hole. Not because the Schwarzschild radius somehow got larger than the star, but because the matter couldn't hold itself up against gravity. And this gravity was weaker than that of a black hole upon collapse.

The math says that low density objects can become black holes.
There are mechanisms that allow low density objects to balance their gravitational collapse.

So - how is it "impossible" for this to happen?

What mechanisms are those? I know of none other than what occurs inside stars.

Normally such a large mass could never find a mechanism to balance it's gravity - however, normally a big star would have exhausted it's internal energy supplies by radiation before it can collapse past it's Schwarzschild radius. In the case of the masses under consideration, it is likely that this will happen before energy sources are gone - so what happens to that energy?

First tell me how a supermassive object like a gas cloud of 150 million solar masses can exist without collapsing under it's own gravity when it begins to approach it's Schwarzschild radius in size.

 

[Simon Bridge]

@vibayjain: that is for a star - for the Sun to become a black-hole it would need to be super-dense first. That is correct. However, a supermassive black hole need not be so dense. You can see this from the math - the Schwarzschild radius is proportional to the mass, but the radius of a spherical lump of matter is proportional to the cube-root of mass.

This means that, for a given density, one can find an amount of mass whose physical radius is the same as the Schwarzschild radius.

It won't be that simple IRL - since you won't get a uniform density. That's just to simplify the thought experiment - just like we do a lot of thought experiments with non-rotating BHs even though these probably don't exist IRL (find a star that doesn't spin - still, I understand it is plausible).

One way SMBHs form is by having big popIII "seed" BHs absorb each other and stars and anything else they can and so join up to make a really big one. If you double the mass, you double the schwarzchild radius, but this increases the volume by eight times ... so the density decreases: it's a quarter what you started with. YOu can keep going and get the density as low as you like.

Or do it the other way - because this suggests that a black-hold could form from a low density accumulation of matter. BA talks about this [#10]:
"A billion solar mass black hole (big, but we see them this big in galaxy centers) would drop that density by a factor of 1 x 10¹⁸. That would give it a density of roughly 1/1000 of a gram per cc… and that’s the density of air! ... A billion solar mass black hole would have an event horizon 3 billion km in radius — roughly the distance of Neptune to the Sun. ... See where I’m going here? If you were to rope off the solar system out past Neptune, enclose it in a giant sphere, and fill it with air, it would be a black hole!"
(Of course - that mass would collapse unless it was also pretty hot - back-of-envelope suggests 8-1000K, which seems awfully cool to me so I don't trust it. Still, see below.)

We could argue that, since the event horizon is right there the space-time geometry means that as a diffuse contracting gas cloud approaches (BA example) air density, it suddenly radiates all it's remaining energy and collapses to a super dense state at the center of it's event horizon.

We could argue that a gas cloud that size and mass cannot possibly sustain itself against it's gravity - there is no possible equilibrium. The mass is so large that it's gravity will eventually overcome even it's pauli pressure.

I'd like to do the math on this.

When a stellar BH forms it has to radiate away a lot of the energy that was previously supporting it in hydrostatic equilibrium. But if the energy could not escape the surface of the star for some reason, wouldn't the star be able to support itself indefinitely?

There are a couple of big ifs here, and I'd like to do the math on them.
1. the contracting cloud does not undergo a sudden collapse when approaching the critical density, allowing an event horizon to appear while the gas is still at quite low densities.
2. no energy escapes the resulting black hole - so the enclosed system is purely adiabatic

So we may ask, if there is a balance point where the mass is big enough for a low-density SMBH but low enough to allow a balance when there are no losses - and, where no equilibrium is possible, how long one may expect the low density state to exist.

We could look at it the other way around too ... what is the space-time geometry inside a spherical matter field of a given density and extent. What happens to this as the extent is increased, keeping the density the same?

At first I thought that such large gas fields could not balance their gravity thermally, so they would have to use up energy in nuclear reactions etc - then I saw that ISM about SMBHs was very close to thermal in the early universe. So it does not seem so far-fetched that the SMBH itself formed from material in a similar state.

I thought that small variations in the density within such a large gas cloud would make bits of it form stars, and stellar-size black holes, so this would never happen. But it turns out that, while this almost always happens, there are ways that a large gas cloud can contract isothermally without forming stars
"In the absence of H2 molecules, the primordial gas in early dark matter haloes with virial temperatures just above Tvir >~ 10⁴K cools by collisional excitation of atomic H. Although it cools efficiently, this gas remains relatively hot, at a temperature near T ~ 8000 K, and consequently might be able to avoid fragmentation and collapse directly into a supermassive black hole."
... that's just one model.Probably Drakkith is correct and total collapse is inevitable. From the pov of an observer outside the nascent SMBH, there would be a huge burst of light to make ordinary supernovas look weak and pale. (The energy release is a consequence of the collapse.) The explosion would clear out the ISM by the SMBH - except maybe an accretion disk for quasars.

I'd still like to see the math.

That's all I'm asking about.

I'm really surprised at the amount of hostility I'm getting I mean: what's wrong with doing the math? I'd have thought something like this would be an exercize for senior undergrad college students somewhere like the BH formation math is in basic GR courses. However, it seems that nobody reading this thread knows of any such thing so I'll have to look elsewhere, maybe do it myself.

Thanks anyway folks.

 

[vinayjain]

I'm really surprised at the amount of hostility I'm getting I mean: what's wrong with doing the math? I'd have thought something like this would be an exercize for senior undergrad college students somewhere like the BH formation math is in basic GR courses. However, it seems that nobody reading this thread knows of any such thing so I'll have to look elsewhere, maybe do it myself.

Thanks anyway folks.

@simon: it does not means like that we are not doing any math but the thing is what we have read and understood till now your statements are contradicting those studies and thus we are just clarifying the whole scenario....

Welcome anyway

 

[vinayjain]

Can anyone tell me that what is the temp. near black hole ?

 

[Nabeshin]

We could argue that a gas cloud that size and mass cannot possibly sustain itself against it's gravity - there is no possible equilibrium. The mass is so large that it's gravity will eventually overcome even it's pauli pressure.

I'd like to do the math on this.

Am I correct in thinking that you'd like to see a proof that there's no stable equilibrium for matter inside its event horizon? Intuitively, all light cones within the event horizon are directed radially inward, thus we can see that the matter cannot remain in equilibrium at a fixed radius (no matter what).


More mathematically:
http://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

 

[vinayjain]

Can anyone tell me that why there is only one supermassive black hole was created in many galaxies while these galaxies were formed not more than one is created during that process