A query about Black Holes

[Farsight]

There's something I'm puzzling about regarding black holes:

 

I think it's reasonable to assume that black holes exist. But we know from GPS and other evidence that clocks run slower here on earth than they do up in space. It's not an optical illusion or some kind of observer effect, it's something real, and it's down to gravity. This means time "runs slower" as you near an event horizon, whereupon it stops. Which suggests to me that collapsing stars are collapsing so slowly as far as our time experience is concerned, that they haven't finished collapsing yet. This means there can't be any actual singularities, because as far as we're concerned, the collapse takes an infinite length of time. And if Hawking Radiation is true, the black hole will evaporate before the collapse is complete.

 

Can anybody clear this up for me?

[InfiniteNow]

It's acceleration that makes time dilate (or run slower/faster), however, that change is relative to an observer elsewhere. The object/person accelerating will not notice any change... They sense time passing as per usual.

 

As one nears an event horizon, they accelerate more and more quickly, hence observers from a distance will notice them going slower and slower, and eventually they will seem to freeze (infinite red-shift).

 

However, the one who approaches the horizon will move on and on, as if nothing were happening.

 

Folks are still working out the math and concepts of singularies and BH collapse, so it's tough to propose a definitive answer (at least, I cannot) for the other questions you posed about evaporating prior to collapse.

 

 

As an aside, a neat little tidbit I've always found fascinating... If a traveller were to cross the event horizon and travel down into a BH, the difference in gravity between their feet and their head would be so great that they'd stretch like a piece of spaghetti and fly apart. Basically, the gravity at their feet is stronger than the gravity at their head, and they'd be stretched by the tidal forces, much like the moon assists in tidal bulges here on Earth.

 

 

Watch out for the Flying Spaghetti Monster Blackholius... They're the worst kind! :D

[Jay-qu]

Im pretty sure you dont have to get beyond the event horizon before tidal forces rip anything apart..

 

To us sitting in normal space it would take an infinite amount of time for something to reach the centre of a black hole, but to the observer it would happen almost instantly and they would reach the end of time :eek:

 

So when you are looking at a black hole, though it may have been around for billions of years, would not have progressed much since collapse.. but this doesnt stop hawking radiation, as that occurs at the event horizen, so it will be very slow relative to us, but not stopped.

[Farsight]

Thanks guys

 

Infinitenow, are you sure about acceleration causing time dilation? I always understood it to be velocity.

 

Jay-qu, does that means no singularities then?

[arkain101]

As an aside, a neat little tidbit I've always found fascinating... If a traveller were to cross the event horizon and travel down into a BH, the difference in gravity between their feet and their head would be so great that they'd stretch like a piece of spaghetti and fly apart. Basically, the gravity at their feet is stronger than the gravity at their head, and they'd be stretched by the tidal forces, much like the moon assists in tidal bulges here on Earth.

 

 

Watch out for the Flying Spaghetti Monster Blackholius... They're the worst kind

However as you accelerate your observations would change would they not? Lets assume you body remains intact as you super accelerate towards the hole. Space would physically contract in the direction of motion as you speed up. Now would your feet take on relativistic effects presuming oyu didnt die in the process.?

 

Its obvsiously a complicated subject.

[Jay-qu]

Im not sure, I think there are arguments either way..

[sebbysteiny]

My general relativity is a little rusty, but I'm not sure the correct response has yet been given.

 

Why does time slow down as you approach a black hole?

 

It's acceleration that makes time dilate (or run slower/faster), however, that change is relative to an observer elsewhere. The object/person accelerating will not notice any change... They sense time passing as per usual.

 

As one nears an event horizon, they accelerate more and more quickly, hence observers from a distance will notice them going slower and slower, and eventually they will seem to freeze (infinite red-shift).

 

I might be wrong but I cannot agree with that reasoning.

 

As you accellarate more and more, time slows down relative to another observer until that observer stops stationary?

 

That's not what I learned from special Relativity. Even if you are accellarating infinately, the maximum velocity you can go relative to another observer is c. So that observer should see you fly straight into the black hole at speed almost c. However it should look to the stationary observer like the observer who is soon to die (the 'shmuch') has his time slowed down so that events to him will seem to happen even quicker than what the stationary observer observes.

 

So if it's not the accellaration, what's happening?

 

The answer, I'm afraid, is found in general relativity.

 

Basically, to cut a long story short, gravity distorts spacetime [ie the universe]. The stronger the mass, the stronger the distortion. The stronger the distortion, the slower time appears relative to an observer in space.

 

So an observer circling Jupiter will see events happening on Jupiter much more slowly. That observer will also age faster.

 

So as the shmuch approaches the event horizen of a black hole, time has slowed down (as measured by an outside observer) so much that time appears to approach zero.

 

So the external observer will see the person falling closer and time slowing down so that the last agonising seconds of that falling observer will be spread out over infinite time. The shmuch will appear to hover stationary at the event horizen.

 

But from the point of view of the shmuch, he will fall straight into the centre of the black hole and die in fractions of a second.

 

Okay, so that's the science.

 

This means there can't be any actual singularities, because as far as we're concerned, the collapse takes an infinite length of time.

 

Not really. The event horizen is a singularity. To calculate what happens to the shmuck, we need to use imaginary time. And we discover only pain awaits. Lots and lots of pain. But the poitn is, the infinite time (and space) at the event horizen means effectively that spacetime, the very fabric of the Universe, breaks down. Hence, a singularity. Beyond the event horizen, space is restorted, if I remember right. But nothing gets beyond when observed from the Universe.

 

And if Hawking Radiation is true, the black hole will evaporate before the collapse is complete.

 

I think you should treat the black hole as having fully collapsed when all the matter held has reached (or is very close to) the event horizon as observed by the outside observer.

 

Lets assume you body remains intact as you super accelerate towards the hole. Space would physically contract in the direction of motion as you speed up. Now would your feet take on relativistic effects presuming oyu didnt die in the process.?

 

Yes. If the shmuch didn't die somehow, then his whole body must be travelling at the same velocity. So the relativistic effects will be equal throughout the shmuch's body and he would seem shorter to the outside observer.

 

If he is allowed to stretch without dying, then, since parts of his body are now at different velocities, lorenz contraction would not be equal and his body would appear even more stretched to the outside observer.

 

But this is all how he looks. He will not feel any of the relativistic stretching. He will only feel the little matter of the gravitational difference which should be more than sufficient for all his fun loving needs.

 

Its obvsiously a complicated subject.

 

It's not so bad if you deal with it qualitively. Calculating the things quantitively though is a right *****. Especially all that imaginary time stuff.

[Qfwfq]

It's how the Schwarzschild metric:

 

[math]ds^2=(1-\frac{2GM}{c^2 r})(c\,dt)^2-(1-\frac{2GM}{c^2 r})^{-1}dr^2-{\rm angular terms}[/math]

 

is interpreted. Notice the coefficient of [math]\norm(c\;dt)^2[/math], compare with the Minkowskian metric of flat space (to which the above tends for large r):

 

[math]ds^2=(c\,dt)^2-dx^2-dy^2-dz^2[/math] (dx = dr)

 

Does that help any? What actually happens crossing the event horizon is wierd, more than anyone could imagine. After crossing it, the t and r directions of space-time have exchanged roles; all outside is the past (no going back) and the future is the centre.

[Farsight]

I have something of an issue with time, Qfwfq. It's all Minkowski's fault, but perhaps this not the place to repeat them. Thanks for the response, which I can read but I can't grasp. I'm left scratching my head. I guess the question I'm asking here is: has anything actually crossed an event horizon yet?

 

Sebby: I'm also beginning to have some issues with the concept of curved spacetime. I can't explain or justify this yet.

[sebbysteiny]

Sebby: I'm also beginning to have some issues with the concept of curved spacetime. I can't explain or justify this yet.

 

You don't really need to unless you study general relativity to a high level.

 

Again, I repeat that my general relativity is a little rusty and I have not looked at a book on the subject for 2 years.

 

But I think the way Einstein justified it was as follows.

 

He came up with the concept of a (non accellerating) inertial frame as the centre piece of special relativity. The idea, he goes, is that the laws of physics do not depend on the particular relative velocity of the inertial frame. Thus, as c is a constant required for many calculations, c must be the same in all frames.

 

But then he thought about applying this in practice. The problem is gravity. There is nowhere in the Universe that is free from the accelleration of gravity. So to get round that, he proposed that the free fall frame IS the same as an inertial frame. But more problems arive as, unless a body is infinitely small, there will be a slightly different gravitational force at different parts of the particular body. Thus there still cannot be a freefall frame.

 

So Einstein got a hunch. His hunch was that there was something more fundamental about gravity. He thought this might be caused by 4d curviture of the universe (aka spacetime). So he spent years learning the mathematics of curviture and applied it to our universe and, with the assumption that mass curves the universe, he came up with a theory that produced an equation that, for small velocities, was identical to Newtons. Further, he predicted a host of other predictions (eg light bending) that were only tested about 10-15 years later (I think). And Einstein's equations were correct.

 

So the way to imagine it without getting into the mathematics is this: what would happen if we were 3 dimensional beings living in a 4D curved universe? How could we tell? To make this simple, imagine we were living in a 2D universe and it was shaped like a sphere. How could we tell? This is effectively what Einstein did to come up with his replacement of Newtonian gravity.

[Qfwfq]

Thanks for the response, which I can read but I can't grasp. I'm left scratching my head.

These are difficult subjects. If you haven't completed advanced courses, it's understandable that you're scratching your head. If you have completed good ones, it still isn't exactly easy to get things straight. :lol:

 

A basic thing about when people say things like "time runs slower" is to understand the sense of it. It's only a shortcut expression, and somewhat misleading, for a comparison between time coordinates according to different observers.

 

I guess the question I'm asking here is: has anything actually crossed an event horizon yet?

So far there have been plenty observations of the effects of material falling into black holes, look up accretion disks.

[arkain101]

I wish I knew how to make words link to sites...

 

Popular,

 

Schwarzschild_metric

http://en.wikipedia.org/wiki/Schwarzschild_metric

[Pyrotex]

... This means time "runs slower" as you near an event horizon, whereupon it stops. Which suggests to me that collapsing stars are collapsing so slowly as far as our time experience is concerned, that they haven't finished collapsing yet. This means there can't be any actual singularities, because as far as we're concerned, the collapse takes an infinite length of time. ...

Excellent question. Your setup information is correct. However, when dealing with Einstein's Theories of Relativity (Special and General) you must always include the words, "as seen by an observer".

 

"time runs slower as you near an event horizon, whereupon it stops" as seen by an observer outside the event horizon.

 

"the collapse takes an infinite length of time" as seen by an observer outside the event horizon.

 

It has been theorized that if we could get close enough to a black hole so that we could see its disk through a telescope, we might be able to see the ghostly infrared images of the last objects to have fallen in, still falling slower and slower as the wavelength of their light gets longer and longer. These ghostly images all summed together comprise the Event Horizon.

 

However, to an observer inside the star, he will observe the star and himself collapse quite quickly and his last living thought will be, "oh ****, it's a singulari...."

 

Oddly enough, if YOU fell in (to a suitable LARGE black hole) you might not even notice it! You could zip right on through the Event Horizon and looking up, you see me (with my giant telescope) moving faster and faster as the light of my image shifts inexorably into the ultraviolet, X-ray, gamma... etc. When you got close enough to the singularity, and yes it would be there, because you're observing from a different frame of reference now, the tidal forces would dismantle you, then dismantle your atoms, and phphpffttt!!!

 

Hawking Radiation is a small process. The formation of a black hole represents zillions of times more energy than HR can give off. A black hole can "evaporate" only if the addition of more matter is practically zero for eons of time.

[Farsight]

Thanks again Qfwfq, and thanks arkain and Pyrotex. This is pretty interesting. Pyrotex, how does this grab you:

 

The collapse takes an infinite time as seen by any observer in the exterior universe, and in comparison to any other observed time in the outside universe.

[InfiniteNow]

I wish I knew how to make words link to sites...

 

[url="www.yourlinkhere.com"]The words you want to act as the link[/url]

[Qfwfq]

I wish I knew how to make words link to sites...

This type of question should be asked in places such as "Tutorials and How-tos", especially if answers couldn't be found by searching through it or by consulting our FAQ, where you could have found the guide to vB code.

[Pyrotex]

[url="www.yourlinkhere.com"]The words you want to act as the link[/url]

 

Thank you, thank you, thank you, oh great purveyor of world wide wisdom and digital dogma. [grovel] :hyper: