How does the size of a black hole affect its ergosphere and event horizon?

[Skhandelwal]

Here is my theory, black hole kept sucking stuff that it got to the point where other black holes started merging in together then later on, everything was concentrated at one point, which caused the big bang. So it really is a cycle. WHat do you guys think?

 

[sdemjanenko]

Hawking radiation prevents this from happening. Over time the black hole just kinda will evaporate. Suppose that all the matter is in the hole, besides getting into the theoretics as to whether our universe exists anymore, quantum mechanics allows for fluctuations in space-time, some of which become particles, particle, anti-particle pair. The black hole can pull cause both to gain momentum, and hence energy. And since that energy must come from somewhere, the black hole is in essence evaporating. Thats the current theory.


For me, my question is doesn't that black hole gain some energy when it sucks in one of the particles? I would assume that most of the time one of them would get pulled in while the other flies off.

 

[Skhandelwal]

Well, if we assume that black hole is being fed till infinity, well, I know that as black hole is being fed, its size doesn't increase, well then, will there come a point when it will big bang or will it continue to consume matter forever? I know there are theories that black hole is taking matter here and leaking it somewhere else but I don't know if they have any evidence for it. Btw, I once heard that black hole is a size of a dust particle but my bro. doesn't believe me and when I searched on internet, they say there are many kinds of sizes.(such as gravity field from where light doesn't escape, real matter, etc.) I am just confuse, can someone help me out?

Also, I don't understand hawking radiation, I mean why does it omit radiation? And when it takes antiparticle(I thought antiparticle doesn't have negative mass as discussed in a different discussion, considering that antiparticle and antimatter are the samething), doesn't it have equal probability of taking a matter in? Which means that even if black hole does decrease its mass by antiparticle(which I don't get), it would regain it w/ equal probability theorem. lol

 

[Danger]

It's pretty complicated, and you probably need Space Tiger or Astronuc or the like to really explain it. To start with, black holes can indeed merge if they come within gravitational capture range of each other. A hole is generally referenced by its mass, so if a 6 solar-mass hole merged with a 4 SM one, the result would be one 10 SM hole. There are several different radii by which the hole can be defined. The one that is most often thought of is the Event Horizon, so named because that is the distance from the centre beyond which no event can be witnessed. The reason for that is that the escape speed exceeds c at that point, so light that would reveal the event can't get out to be seen.
Hawking radiation comes from the Ergosphere. That is the point at which an object can gain energy from the hole. If a rock with 500 units of energy were to split in half at that point, one piece could fall into the hole and contribute 250 units to it. The other, conversely, could snipe 300 units from the hole and bugger off. The net loss to the hole would be 50 units. In Hawking radiation, pair production of particles from pure energy occurs at the ergosphere. One particle falls in, but the other makes a run for it and takes some of the hole's energy with it. In that manner, the hole can 'evaporate'.

 

[Skhandelwal]

I still don't get that 250 units turning into 300. How does that happen?

 

[Labguy]

It's pretty complicated, and you probably need Space Tiger or Astronuc or the like to really explain it. To start with, black holes can indeed merge if they come within gravitational capture range of each other. A hole is generally referenced by its mass, so if a 6 solar-mass hole merged with a 4 SM one, the result would be one 10 SM hole.

No, when two BH's merge, the remaining mass will always be less than the sum of the two. A large amount of gravitational energy is lost as a result of the merger, and since energy = mass, some mass will be lost.

There are several different radii by which the hole can be defined. The one that is most often thought of is the Event Horizon, so named because that is the distance from the centre beyond which no event can be witnessed. The reason for that is that the escape speed exceeds c at that point, so light that would reveal the event can't get out to be seen.
Hawking radiation comes from the Ergosphere.

Actually, Hawking Radiation (HR) "comes from" the edge of the Event Horizon (EH) which is the classical 2GM/c². This EH is at the same radius for a rotating BH as it is in the classical (non-rotating) BH. But, all BH's rotate and that is where the Ergosphere comes in. Roy Kerr showed that a rotating BH also has a "second" EH, the ergosphere, in the shape of an oblate spheroid with the ergosphere and the EH meeting at the poles of the axis of rotation. Anywhere off the poles and the EH is "inside" the buldge of the ergosphere, so you can visualize the BH as having two EH's. A particle, and photons, between the EH and the ergosphere can escape the BH since the "inside" EH is actually where the radius = the escape velocity of c.

Forgeting the ergosphere for the moment, an old post of mine (on HR and EM production)was:

This (vacuum fluctuation) energy will produce virtual-particle (VP) pairs and not just electrons as has been mentioned so far. The VP pair is produced by "borrowed" energy from the BH. The Heisenberg uncertainty principle allows for two things here. (1) It allows the VP pair to exist on borrowed energy for a finite, but very short, period of time, and (2) it allows the VP pair to be of any energy amount as long as, again, anything borrowed is returned. Therefore, the VP pair is not limited to just electrons and positrons being discussed so far, it can also be quarks, protons, neutrons, and certain mesons regardless of energy required to produce the pair.

So, one of the "virtual" particles falls back into the BH and the other becomes a "real" particle with real mass. If it escapes into space (sometimes both will fall back in), then the mass of whatever the escaping particle was will exactly match the mass-loss of the BH. Mass is delivered into the realm of real and the BH loses that much mass, so the first two laws of thermodynamics are still happy, nothing has been violated.

How does a small BH become so hot and evaporate so fast? Well, the "standard" HR process just mentioned was about one, single VP pair. In a large BH idling along this might be the case here and there around the EH. But, in a smaller BH with more energy per square^anymeasure will be producing VP pairs, of many different particle types, at a great pace. Now we have a swarm of real particles buzzing all around the EH at a very high density. Some will combine into more complex particles, but most will just escape or, to produce the intense energies mentioned, many particle-antiparticle pairs will meet and annihilate into pure energy. If the density is high enough and the particles massive enough, you will see the gamma-ray production Chronos mentioned, again, especially from small, short-lived BH's. Of course, it is actually the entire EM spectrum of photons, and many particles, that are produced but the gamma rays get the most attention.

so, in a rotating BH, particles are produced between the classical EH and the ergosphere, and that is where an object (any mass + photons) CAN escape back into the space away from the BH.

In Hawking radiation, pair production of particles from pure energy occurs at the ergosphere. One particle falls in, but the other makes a run for it and takes some of the hole's energy with it. In that manner, the hole can 'evaporate'.

True except that it is not the ergosphere as explained above.

As far as the ergosphere in concerned, it is this space (area) between the EH and the ergosphere where an object approaching the BH can gain energy and exit with more energy than it had on approach. This is as long as it does not also enter the EH and be lost forever. This effect, not Hawhing Radiation, can also cause the BH to lose mass, but, the energy added to an escaping particle in this case is provided by the angular momentum of the BH. And, since the BH loses angular momentum, it loses energy. Once again, a loss of energy = a loss of mass since mass = energy.

Gets confusing, don't it..

 

[Skhandelwal]

1. When 2 black holes merge, how is the energy lost? In order for energy to loose, it needs to go away, but I thought black hole doesn't allow that to happen?

2. I know ergosphere is the outer layer but what is the diff b/w ergosphere and event horizon?(is it that when light comes in ergosphere, it bends but when it comes to even horizon, it never returns?

3. What causes the gap b/w two?

4. But the same question again, if black hole accepts antiparticle, shouldn't it have the equal probability of accepting particles? Which would equal the weight of the black hole.

 

[Danger]

Oops...
Sorry for the misinformation. It's been a very long time (couple decades) since I've paid much attention to these things. The mind slips. Thanks for the correction, Labguy.
I'll just be slinking back to Engineering now...

 

[Skhandelwal]

Any answers? Please?

Here is an added question on top: If black hole sucks a 2 gram copper and 2 million grams of gold, they both would turn into 0 volume, infinite density. Then what would the diff b/w those two remain? (diff. of how much energy each converts to from mass? Since we can't really say one's mass is bigger than the other b/c both of them turns into infinite density, but may be, if we convert that mass into energy, we can find the differene.) What do you think?

 

[MeJennifer]

Any answers? Please?

Here is an added question on top: If black hole sucks a 2 gram copper and 2 million grams of gold, they both would turn into 0 volume, infinite density. Then what would the diff b/w those two remain? (diff. of how much energy each converts to from mass? Since we can't really say one's mass is bigger than the other b/c both of them turns into infinite density, but may be, if we convert that mass into energy, we can find the differene.) What do you think?

Beyond the Chandrasekhar limit there is no point to talk about different elements anymore. Protons and electrons simply collapse into each other since the gravitational pull is bigger than the effect of Pauli's exclusion principle on fermions.

 

[Skhandelwal]

What is the difference b/w a small black hole and big?(size?) B/c I thought that black hole's size is like the object it sucks which is like zero volume, infinite density.(excluding the event horizon and ergosphere, just the size where the objects really are.)

Oh I get it, bigger black holes have larger ergosphere, the distance b/w ergosphere and event horizon and event horizon, right?