How many dimensions are there in a black hole

[vinayjain]

Can anyone tell me that how many dimensions are there in a black hole and which are the dimension

 

[Simon Bridge]

The usual mathematics of black-holes has four dimentions.
Have a read through:
http://cosmology.berkeley.edu/Education/BHfaq.html
... covers the usual, makes sure you are up to speed.

http://members.cox.net/jhaldenwang/black_hole.htm
... covers the geometry inside and close outside a black-hole.
Executive summary: inside a black hold you get 3 time-like dimensions and one space-like.
You need to read the preamble carefully to understand this.

 

[vinayjain]

can u please tell me the name of those four dimensios which exists in black hole

 

[Simon Bridge]

I just did: after "executive summary" in post #2.
3 time-like and 1 space-like.

If you want to know what that means you'll just have to read the links.
There's no royal road for this one - sorry.
Perhaps if you told me what you want to know for?

 

[vinayjain]

thank you very much for the quick and fruitful reply and I did not want specially anything I am just curious to know about black holes...again a heartest thanks

 

[alzheimer]

those are very useful informations and links, thanks to all, keep it up..

 

[Simon Bridge]

No worries and happy hunting :)

I find that pairing references like this can help - the Berkely FAQ will help refine questions. You get all the way through it and you have a chance of understanding the Haldenwang paper ... even if you don't follow the math.

 

[Simon Bridge]

No worries and happy hunting :)

I find that pairing references like this can help - the Berkely FAQ will help refine questions. You get all the way through it and you have a chance of understanding the Haldenwang paper ... even if you don't follow the math.

 

[vinayjain]

can anyone please clarify my doubt related to black hole i.e. when black suck objects inside event horizon it hits singularity but it obtain some space in black hole then it must lead to a conclusion that the size of black need to be increased as time pass (when black hole is in active mode) so this means that supermassive black hole has gone through this process and hence quasar is formed. please clarify

 

[mkarger]

There's a massive distance between the event horizon (which is nothing more than an optical barrier) and the hypothesized singularity.

There are theories about how black holes both accrete and shed mass. But that is not necessarily related to the formation of quasars.

Quasars are formed from the accretion disk surrounding black holes. They are considered to be early objects within the time span of universal expansion.

 

[vinayjain]

There's a massive distance between the event horizon (which is nothing more than an optical barrier) and the hypothesized singularity.

There are theories about how black holes both accrete and shed mass. But that is not necessarily related to the formation of quasars.

Quasars are formed from the accretion disk surrounding black holes. They are considered to be early objects within the time span of universal expansion.

The thing is this that there is massive distance between event horizon and hypothesized singularity of a massive black hole but when a black hole is not that big then these forces act very soon...

 

[vinayjain]

and related to formation of quasar that is what i am asking if a small black hole suck lots of things its mass could increase and thus there is a formation of accretion disk and thus quasar is that is the process?

 

[Drakkith]

and related to formation of quasar that is what i am asking if a small black hole suck lots of things its mass could increase and thus there is a formation of accretion disk and thus quasar is that is the process?

Sure. How do you think quasars initially formed? The only problem in todays time is that one of the only places there is a high enough concentration of mass to form a quasar is in the center of a galaxy. Which usually happens to already have a supermassive black hole that has already absorbed most of that mass. So we don't really have the conditions to form many quasars at this point in time.

 

[Chronos]

A quasar could care less about the presumed 'singularity'. All the radiation is emitted from outside the event horizon, as has already been noted.

 

[Drakkith]

can anyone please clarify my doubt related to black hole i.e. when black suck objects inside event horizon it hits singularity but it obtain some space in black hole then it must lead to a conclusion that the size of black need to be increased as time pass (when black hole is in active mode) so this means that supermassive black hole has gone through this process and hence quasar is formed. please clarify

As the mass of a black hole increases, the radius of the event horizon from the center also increases. It is currently unknown about the ultimate fate of matter and energy that falls into a black hole and passes the event horizon, so no one can really say much about the singularity.

 

[Simon Bridge]

How long would it take for something to enter a black hole, from the pov of someone well outside it?

NOte: smallest BH found has about 12km to the center, and the biggest (stellar) BH has 50-odd kms. Not that far.

The galactic-center supermassive is supposed to be 13-14million kms to it's center so there you'd be traveling a while. There is a tendency to think of these things as super-dense as well, like stellar BHs, but that need not be the case.

 

[vinayjain]

according to the different studies given on internet it is said that according to the observer who is looking at a black hole it would take a huge amount of time which is considered to be as forever but on the other hand the thing which is falling in the black hole (supermassive) it would take around 7 seconds to hit singularity and for black hole (small in size) gravitational pull will tear the object apart before even entering the black hole.

 

[vinayjain]

As the mass of a black hole increases, the radius of the event horizon from the center also increases. It is currently unknown about the ultimate fate of matter and energy that falls into a black hole and passes the event horizon, so no one can really say much about the singularity.

Probably the thing is when a black hole pulls enough things inside that can increase its radius to an extent where the end side escape velocity is less than velocity of light we see that there is an object emmitting light but actually it is the black hole which has increased its size to that extent (and it may true that's how a quasar is generated)

 

[vinayjain]

can anyone please tell that is it possible that even black holes magnetic poles inside it

 

[Simon Bridge]

BHs can have mass, spin, entropy and charge ... spinning charged hole will have a magnetic field. This would be a Kerr Black Hole. You can also get a magnetic field without spin ... see:
http://burro.cwru.edu/stu/advanced/stars_blackhole.html

As for magnets inside them - Haldenwang
http://members.cox.net/jhaldenwang/black_hole.htm
- discusses the possibility of our Universe being inside a BH. That would include magnets.

If it takes an infinite time for an object to cross into a BH, viewed from a outside, then in what sense would a BH increase it's mass over time?

 

[Drakkith]

Probably the thing is when a black hole pulls enough things inside that can increase its radius to an extent where the end side escape velocity is less than velocity of light we see that there is an object emmitting light but actually it is the black hole which has increased its size to that extent (and it may true that's how a quasar is generated)

I don't think any of that is correct. To my knowledge once inside the event horizon (which is what is expanding when the black hole increases in mass) it is not possible for anything to get back out.

 

[Drakkith]

If it takes an infinite time for an object to cross into a BH, viewed from a outside, then in what sense would a BH increase it's mass over time?

Perhaps the in-falling mass adds to the mass of the black hole (or rather the strength of the gravitational pull in the area around it) making the event horizon expand? Not sure.

 

[vinayjain]

I don't think any of that is correct. To my knowledge once inside the event horizon (which is what is expanding when the black hole increases in mass) it is not possible for anything to get back out.

the statement which i made might be incorrect on which u quoted sir but the thing is if anything cannot come out after crossing the event horizon then how could the gases at accretion disk gets heated up in quasar which have a supermassive black hole at centre...

 

[Drakkith]

the statement which i made might be incorrect on which u quoted sir but the thing is if anything cannot come out after crossing the event horizon then how could the gases at accretion disk gets heated up in quasar which have a supermassive black hole at centre...

The accretion disk is outside of the event horizon.

 

[Nabeshin]

Perhaps the in-falling mass adds to the mass of the black hole (or rather the strength of the gravitational pull in the area around it) making the event horizon expand? Not sure.

Indeed, the event horizon begins to expand BEFORE the mass crosses the horizon from an outside observer's perspective (as noted, it will never do so). The event horizon's size increases asymptotically to the value it would have if we just assumed the the object fell in immediately.

 

[vinayjain]

The accretion disk is outside of the event horizon.

I know that accretion disk is outside the event horizon I am asking that how does the gases present in accretion disk heats up and radiate so that it make the visible from millions of light year and named as quasar.

Means there is a phenomena that heats up the gases to an extent that they radiated...

 

[vinayjain]

If it takes an infinite time for an object to cross into a BH, viewed from a outside, then in what sense would a BH increase it's mass over time?

actually it takes infinite time on the perspective of an outside observer but actually it takes a very short amount of time to fell in black hole after crossing event horizon...

 

[Drakkith]

I know that accretion disk is outside the event horizon I am asking that how does the gases present in accretion disk heats up and radiate so that it make the visible from millions of light year and named as quasar.

Means there is a phenomena that heats up the gases to an extent that they radiated...

From wikipedia:

The most spectacular accretion discs found in nature are those of active galactic nuclei and of quasars, which are believed to be massive black holes at the center of galaxies. As matter spirals into a black hole, the intense gravitational gradient gives rise to intense frictional heating; the accretion disc of a black hole is hot enough to emit X-rays just outside of the event horizon. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. This process can convert about 10 percent of the mass of an object into energy as compared to around 0.5 percent for nuclear fusion processes.

Here's the article: http://en.wikipedia.org/wiki/Accretion_disk

 

[mkarger]

I know that accretion disk is outside the event horizon I am asking that how does the gases present in accretion disk heats up and radiate so that it make the visible from millions of light year and named as quasar.

Means there is a phenomena that heats up the gases to an extent that they radiated...

The accretion disk heats up because it's being compressed.

 

[vinayjain]

The accretion disk heats up because it's being compressed.

How?

 

[Drakkith]

How?

When a material, especially a gas, is compressed it heats up.

 

[mkarger]

How?

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)

 

[mkarger]

Forgot to mention drag friction. A critical component.

Because of conservation of angular momentum, the matter stretches out as it spins. Like pizza dough. Which causes gravity to pull at different strength in different parts of the spinning matter. Because the disk does not act as a solid body, these forces cause a lot of differential speeds. Which results in large amounts of friction loss in the form of light and heat.

 

[Simon Bridge]

actually it takes infinite time on the perspective of an outside observer but actually it takes a very short amount of time to fell in black hole after crossing event horizon...

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?

 

[Simon Bridge]

It is probably safe to say that there are many mechanisms by which a gas will glow brightly in a region of high gravity without actually entering a black hole. Ordinary stars seem to manage it. The gravity gradient near a BH is much greater so it is reasonable to expect the gas there to get very bright indeed.

 

[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?