One Question About Black Holes

[michaeljohn]

Wouldn't the very center of black holes have zero gravity? For example, if I was at the very center of the Earth wouldn't I be weightless because the pull of gravity was equal and opposite in all directions? Wouldn't this be true for any massive body including black holes? And of course I am not talking about surviving in it or anything crazy like that but wouldn't the spacetime curve look more like a buntcake than an oil funnel? If that is the case could a black hole have a very very small clear spot at its very center that an observer could see through to it's other side? And yes, even at the center of Earth you still have the moon and sun and everything else but I am simply interested in the principle. Thanks!

 

[Mike Cookson]

Is there a centre to a singularity? I wouldn't have thought so.

 

[my_wan]

Yes if you get also get inside that singularity without getting squashed. Unfortunately a singularity is awful tiny to be trying to get inside of.

 

[michaeljohn]

To be more clear: I am asking if there is in fact a singularity in a black hole. According to Wikipedia:"A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite." So my question is: Is the gravitational field inifinite (a singularity) or zero (flat space) at the center of a black hole (or the coordinates which would lead to a center for a black hole)? Or can you have an infinite gravitational field and still be in zero gravity? Thanks again for any posts!

 

[my_wan]

A singularity is defined (in a black hole) by a mass of infinite density and zero size at the center. The gravitational field itself is not infinite anywhere except this one point in the middle. Quantum Mechanical effects might dissolve this singularity, we simply don't know. General Relativity by itself predicts this singularity. We can't call the singularity itself a fact, just the prediction of them based on a theory that makes very good predictions elsewhere. Including black holes themselves.

Because this black hole mass is at the center with no size the gravitational field can't be zero anywhere on or near it. The only time gravity is zero inside a gravitational well is if the mass is equidistantly distributed around you. A mass point doesn't allow this. However, it doesn't really matter how strong the gravitational field is, if you are inside the mass defining it the gravity is zero, though time dilation may be extreme. If the mass is in a sphere like a very large massive beach ball then the gravity will be zero anywhere inside it, not just in the middle.

There is a lot we don't know and can't even directly test. All we can can do is test the predictions of the theory that we can observe.

 

[LURCH]

To elaborate on what My_Wan said:

Theoratically, if you could get to the center, or the "inside," of a singularity...

1) Yes, gravitational forces would be "zero"

2) It wouldn't be a singularity. A singularity is a single point, it doesn't have an "inside" or a "center"; it is the center. So, one can be "outside" the singularity, or "at" the singularity, but one can never be "inside" the singularity.

 

[Nabeshin]

Here's one to wrap your minds around: As a star collapses to form a black hole, time dilation effects will increase as the black-hole-to-be increases in density. So, the closer it gets to forming a singularity, the more time should slow down for the in-falling matter (relative to an outside observer). So, it should seem that the matter should never get there at all to form the singularity! Of course this is untestable because the singularity would be inside the event horizon, and nobody likes naked singularities. Thoughts?

 

[MeJennifer]

Wouldn't the very center of black holes have zero gravity?

A black hole as modeled by the Schwarzschild solution has no center.

 

[LURCH]

Here's one to wrap your minds around: As a star collapses to form a black hole, time dilation effects will increase as the black-hole-to-be increases in density. So, the closer it gets to forming a singularity, the more time should slow down for the in-falling matter (relative to an outside observer). So, it should seem that the matter should never get there at all to form the singularity! Of course this is untestable because the singularity would be inside the event horizon, and nobody likes naked singularities. Thoughts?

Exactly the same conclusion I have reached, Nabeshin. So, it would seem to me that a true singularity (naked or otherwise) cannot really exist. At the center of a black hole, there is a star "frozen" in the final stages of collapse, which continually approaches, but never reaches, true singularity. So I speculate that, it sometime in the very distant future, talking radiation will evaporate the black hole until the mass inside the event horizon is no longer sufficient to be a black hole.

So the next question becomes, when the gravitational forces at the center of the black hole are no longer strong enough to overpower the Pauli exclusion principal, or electron degeneration, what will that sinful mass do? My best guess is that it would expand quite violently.

 

[MeJennifer]

A test particle falling into a black hole reaches the singularity in a finite proper time.

 

[Nabeshin]

A test particle falling into a black hole reaches the singularity in a finite proper time.

Intuition? Have you measured this?

 

[Wallace]

MeJennifer is correct, in the Schwarzschild (and related) black hole solutions in falling observers reach the singularity in a finite time. In fact an in falling observer really wouldn't notice anything particularly strange as the pass the event horizon even (well no stranger than the bizarre effects you'd see and feel near a black hole but outside the horizon anyway).

 

[Nabeshin]

MeJennifer is correct, in the Schwarzschild (and related) black hole solutions in falling observers reach the singularity in a finite time. In fact an in falling observer really wouldn't notice anything particularly strange as the pass the event horizon even (well no stranger than the bizarre effects you'd see and feel near a black hole but outside the horizon anyway).

Ok, I agree that the falling object (or observer) will observe no time dilation and will themselves reach the singularity in a finite time. But it seems that's just one reference frame, because to them (of course they can't but bare with me here) the rest of the universe accelerates until the end of time, if you understand what I'm saying. In other words, to the outside observer (who of course can't observe this) the observer would never reach the singularity.

Now, I'm a bit hazy on this point. To me this makes sense only if the observation is casual side effect. If, however, it presents a real obstacle, what I'm saying is obviously groundless.

 

[MeJennifer]

But it seems that's just one reference frame, because to them (of course they can't but bear with me hear) the rest of the universe accelerates until the end of time, if you understand what I'm saying.

It is interesting to note that black holes do not exist in closed universes, only open universes can have black holes. Think in this context about diffeomorphism invariance, open and closed universes are of incompatible "form".

 

[LURCH]

A test particle falling into a black hole reaches the singularity in a finite proper time.

But time will pass differently for them than for the rest of the universe, yes? So, as has been mentioned above, it would seem that the infalling observer sees no particular change in themselves, but the rest of the universe would appear to "speed up" considerably. As the universe rapidly ages, the BH evaporates. This causes it to lose mass, which in turn causes its radius to decrease. So, if the infalling observer could "see" the event Horizon, would it not appear to be catching up to them from behind, until it overtakes them in a finite time that is less than the finite time it would have taken them to reach the center of the black hole?

From their perspective, this may all happen in a few minutes as the free fall from the event Horizon toward the center of the black hole. However, in those few minutes the universe would have aged billions of years and the black hole would have evaporated down to microscopic size, disappearing before they ever reached the center.

BTW: Sorry about the reference to "talking radiation" in my earlier post; inside joke that I forgot to edit out.

 

[MeJennifer]

As the universe rapidly ages, the BH evaporates. This causes it to lose mass, which in turn causes its radius to decrease. So, if the infalling observer could "see" the event Horizon, would it not appear to be catching up to them from behind, until it overtakes them in a finite time that is less than the finite time it would have taken them to reach the center of the black hole?

This is possible.

 

[Nabeshin]

But time will pass differently for them than for the rest of the universe, yes? So, as has been mentioned above, it would seem that the infalling observer sees no particular change in themselves, but the rest of the universe would appear to "speed up" considerably. As the universe rapidly ages, the BH evaporates. This causes it to lose mass, which in turn causes its radius to decrease. So, if the infalling observer could "see" the event Horizon, would it not appear to be catching up to them from behind, until it overtakes them in a finite time that is less than the finite time it would have taken them to reach the center of the black hole?

From their perspective, this may all happen in a few minutes as the free fall from the event Horizon toward the center of the black hole. However, in those few minutes the universe would have aged billions of years and the black hole would have evaporated down to microscopic size, disappearing before they ever reached the center.

BTW: Sorry about the reference to "talking radiation" in my earlier post; inside joke that I forgot to edit out.

This makes sense to me. However, this should apply to all matter that ever fell into a black hole, no? So when the black hole evaporates, should not everything it ever consumed be re-emitted into space? Perhaps none have simply decayed yet (I understand hawking radiation to be a painfully slow process for large black holes). Additionally, if nothing ever reaches the center of the black hole in this fashion, where does the lost mass via hawking radiation come from? Infalling matter?