Black hole, schwarzschild radius, etc

[Baby Astronaut]

A few questions popped up while reading answers in the other thread related to black holes. I then looked up schwarzschild radius, and even more questions popped up -- hope someone can oblige.

 

 

1) Is a black hole's radius smaller than an elementary particle or atom's radius?

 

2) Gravity is supposed to be the weakest force. Yet a black hole is pretty damn strong. Light can't even escape it. Therefore, if the other forces are stronger than gravity, can each one prevent light from escaping too?

 

3) Once the schwarzschild radius is fulfilled, the ensuing collapse of mass is unstoppable by any known force. How is that possible if the other forces are stronger than the gravity responsible for the collapse?

 

4) Also: what if an object's schwarzschild radius were fulfilled just as it crossed the event horizon of a neighboring black hole...wouldn't that actually prevent the object's collapse? I'm thinking of the same mechanism for black hole evaporation, where virtual particles are split at the event horizon. In the same manner, wouldn't a collapsing object be split apart during the process -- before it entirely collapsed?

 

5) Is space able to expand within a black hole (i.e. cosmic expansion)? I just mean space itself, not any objects "carried" by space during its expansion.

[ajb]

1) Is a black hole's radius smaller than an elementary particle or atom's radius?

 

Classically the singularity is a point. We can (non-technically) define it to be a point for which the curvature tends to infinity as you approach that point. (It is a bit more work to define this carefully).

 

As a point it has no dimensions. However, no-one really believes that the curvature really tends to infinity inside a black hole. It is expected that quantum effects will smear out the notion of a point and regulate the curvature so that it is nowhere infinite.

 

2) Gravity is supposed to be the weakest force. Yet a black hole is pretty damn strong. Light can't even escape it. Therefore, if the other forces are stronger than gravity, can each one prevent light from escaping too?

 

I see in principle no reason why not. Photons can interact with all the other carrier bosons, gravitationally, electromagnetically, strongly and weakly, even if this is a loop process which would suppress these interactions. Maybe someone who is more of an expert in the standard model could say more here

 

3) Once the schwarzschild radius is fulfilled, the ensuing collapse of mass is unstoppable by any known force. How is that possible if the other forces are stronger than the gravity responsible for the collapse?

 

You have confused the idea of the strengths of the forces. This is not the "absolute" but really compares there "natural scale".

 

So if something is massive enough the gravity can overcome its electromagnetic forces supporting it, for example.

 

4) Also: what if an object's schwarzschild radius were fulfilled just as it crossed the event horizon of a neighboring black hole...wouldn't that actually prevent the object's collapse? I'm thinking of the same mechanism for black hole evaporation, where virtual particles are split at the event horizon. In the same manner, wouldn't a collapsing object be split apart during the process -- before it entirely collapsed?

 

Black holes can merge. But your question is more than that.

 

I don't know if (or how) the situation you suggest effect black hole mergers.

 

However, what I will say is that the Bekenstein-Hawking radiation is not really explained using virtual pairs. There is no calculation that uses that notion. It's origin is really in the fact that we lose the notion of a unique vacuum state. This in effect messes up the usual tools of quantum field theory for particles.

 

5) Is space able to expand within a black hole (i.e. cosmic expansion)? I just mean space itself, not any objects "carried" by space during its expansion.

 

If you look at the thermodynamics of a black hole, you find that the area of the horizon is a non-decreasing function of time.

 

So, if you "feed it" the horizon can get bigger.

[Baby Astronaut]

On #3's answer I follow you, on the rest I don't quite.

 

Also...for #4, I was just referring to one black hole, not two of them. Because the object at the event horizon is about to form a black hole -- it just hasn't yet, as it's only in the beginning phase of schwarzschild-type collapse, which is unstoppable by all known forces. Except, perhaps, if half of the starting-to-collapse object were at that very moment passing an event horizon, while its other half is still outside the event horizon. So my question is: can that situation halt the "unstoppable" collapse?

 

You sort of answered that one with #3, yet the situation I'm presenting is on a "natural scale" (even if the chances of it occurring are severely limited).

 

However thanks for your reply and help so far.

[ajb]

I should have asked by the black hole's radius do you mean the radius of the horizon or the radius of the "object" causing the black hole?

 

You can calculate via the Schwartzchild metric the mass needed to have a horizon radius comparable to the atomic size.

 

Importantly for black holes we have the no hair theorem. This states that a black hole is characterised by mass, angular momentum and electric charge. Thus, if we were to "feed" a black hole with something about to form a black hole itself as soon as it touches the horizon we would not know if it formed a black hole or not. Presentably, an observer falling in to the black hole could tell. Then, we have the huge tidal forces to deal with. So honesty, I don't know the answer to your question.

[Baby Astronaut]

I should have asked by the black hole's radius do you mean the radius of the horizon or the radius of the "object" causing the black hole?

The object causing it, so ignore the horizon (in relation to comparing sizes of a black hole and elementary particles).

 

Importantly for black holes we have the no hair theorem...

Sure, I get it. No information can escape from beyond the horizon.

 

But what about the part of it that's outside the horizon? Let's say this object's even identical to our sun, but compacted to 3 km -- its schwarzschild radius, I believe. And its compaction occurred at the exact moment that nearly 1 km of the star crossed the event horizon, yet it's careening through space at high enough velocity that its "outside" 2 km portion wouldn't fall into the black hole -- due to the angle of its trajectory and the position at which it brushed the event horizon -- thus its outer portion would continue traveling (away from the black hole).

 

We'd still be able to tell what happened to a collapsing object this side of an event horizon. Does it collapse all the way anyway, or does the collapse process simply just dissipate midway?

 

Here's what I'm ultimately saying: the collapsing portion within our side is in a tug-of-war between its "unstoppable" gravitational collapse and the other side's "point-of-no-return" gravitational black hole tug.

Edited July 12, 2009 by Baby Astronaut

[ajb]

The object causing it, so ignore the horizon (in relation to comparing sizes of a black hole and elementary particles).

 

It is believed you can have atomic and sub atomic sized horizons.

 

Now, as to the size of the object, classically it is a point. However, as I said in my first reply no-one really thinks that all the matter/mass of a star becomes concentrated at a "real point". Quantum theory should sort this out.

 

 

 

Sure, I get it. No information can escape from beyond the horizon.

But what about the part of it that's outside the horizon? Let's say this object's even identical to our sun, but compacted to 3 km -- its schwarzschild radius, I believe. And its compaction occurred at the exact moment that nearly 1 km of the star crossed the event horizon, yet it's careening through space at high enough velocity that its "outside" 2 km portion wouldn't fall into the black hole -- due to the angle of its trajectory and the position at which it brushed the event horizon -- thus its outer portion would continue traveling (away from the black hole).

 

We'd still be able to tell what happened to a collapsing object this side of an event horizon. Does it collapse all the way anyway, or does the collapse process simply just dissipate midway?

 

Here's what I'm ultimately saying: the collapsing portion within our side is in a tug-of-war between its "unstoppable" gravitational collapse and the other side's "point-of-no-return" gravitational black hole tug.

 

Half in half out situation. Despite the fact that is a very contrived set up, it is an interesting question. I am sure experts in GR have discussed similar situations, maybe feeding things in on ropes for example. I don't known.

[Baby Astronaut]

Bumping to see if anyone has further info to contributre.

 

 

A star just beginning to collapse has passed 1/3 way into the event horizon of a black hole. The star's velocity and angle keeps the rest of it from entering the black hole as the collapse occurs.

 

A tug of war is occuring between the star's 1/3 material inevitable collapse towards its center outside the BH's horizon, and the point-of-no-return gravitational tug of the black hole on that same 1/3.

 

 

Although my scenario's improbable, and highly so, is the occurrence itself -- the tug of war described above -- is that impossible, such as it wouldn't have any chance of occurring any way?