Does an event horizon ever exist?

[Mordred]

As its related another favourite article I have in my database lol this one has been posted by otheres a few times but it covers a falling observer toward the EH

http://www-e.uni-magdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf

 

[photonkid]

I am not sure why this question wasn't answered but just as a link:
http://en.wikipedia.org/wiki/Sagittarius_A*

yeah, I had seen that but I hadn't read much of it ... but now I have.

It says - a 2008 study ... <quote> delivered "what is now considered to be the best empirical evidence that super-massive black holes do really exist. The stellar orbits in the galactic centre show that the central mass concentration of four million solar masses must be a black hole, beyond any reasonable doubt." </>

So if it's a black hole it must have an event horizon.

The article then says <quote> While, strictly speaking, there are other mass configurations that would explain the measured mass and size, such an arrangement would collapse into a single supermassive black hole on a timescale much shorter than the life of the Milky Way. </>

But, if time slows down inside the event horizon and "almost stops" relative to the vast majority of the universe, how could a black hole ever form?

The guy who solved Einsteins equations for rotating black holes (Roy Kerr) plays at my local bridge club and I *think* he told me that an event horizon doesn't exist because it takes an infinite amount of time to form.

 

[Passionflower]

The guy who solved Einsteins equations for rotating black holes (Roy Kerr) plays at my local bridge club and I *think* he told me that an event horizon doesn't exist because it takes an infinite amount of time to form.

Which is not a problem provided spacetime is open if it is closed it can never completely form.

I am often flabbergasted by the 'stiff upper lip' double standard attitude. When it comes to the Schwarzschild solution an observer passing the event horizon is A-OK 'because the math shows it', but when we start talking about a Kerr solution and an observer goes into the ergosphere or beyond it is suddenly 'obviously' no longer physical.

 

[Mordred]

Which is not a problem provided spacetime is open if it is closed it can never completely form.

What ?you lost me on that one.

 

[Passionflower]

What ?you lost me on that one.

You might want to read:
http://arxiv.org/abs/gr-qc/0003082

 

[photonkid]

Which is not a problem provided spacetime is open if it is closed it can never completely form.

I am often flabbergasted by the 'stiff upper lip' double standard attitude. When it comes to the Schwarzschild solution an observer passing the event horizon is A-OK 'because the math shows it', but when we start talking about a Kerr solution and an observer goes into the ergosphere or beyond it is suddenly 'obviously' no longer physical.

When Roy Kerr told me an event horizon doesn't exist, he also immediately said "we don't know what happens inside a black hole". I was taken by surprise and may have misheard what he said - but he did say that there is a black hole at the center of the milky way. Hence I'm trying to find out what a black hole is. Is it just a large concentration of mass - or does it have special observable properties other than what a "large concentration of mass" would have.

 

[photonkid]

yeah, I had seen that but I hadn't read much of it ... but now I have.

It says - a 2008 study ... <quote> delivered "what is now considered to be the best empirical evidence that super-massive black holes do really exist. The stellar orbits in the galactic centre show that the central mass concentration of four million solar masses must be a black hole, beyond any reasonable doubt." </>

And now that I look at the "talk page" for the Wikipedia article,
http://en.wikipedia.org/wiki/Talk:Sagittarius_A*#There_is_no_evidence_to_support_that_it_.22must_be_a_black_hole_beyond_any_reasonable_doubt.22
someone says

<quote> There is no evidence proving that it is a black hole. There is only evidence that it is a supermassive object somewhere nearby but it's size is not known. </>

And someone else on the talk page says this
<quote> Small, dense, with lensing does not require the conclusion that it is a singularity. The point being there may be additional states of matter beyond neutron/quark densities but less than the infinities of a singularity. </>

I think it's strange that most articles on black holes never mention that the idea of a singularity is just a theory and that what actually happens when mass collapses into itself is completely unknown.

 

[PeterDonis]

You might want to read:
http://arxiv.org/abs/gr-qc/0003082

Ah, Tipler and his Omega Point spacetime. He wrote a whole book called The Physics of Immortality based on it. I've always like John Walker's review:

http://www.fourmilab.ch/documents/tipler.html

which includes the priceless quote: "[W]e're twiddling the Higgs field to make the whole bloody universe collapse asymmetrically, with the whole universe becoming a delay line memory."

(Note: as far as I can tell, the Omega Point spacetime is a valid solution to the EFE, mathematically speaking; it just has some pretty unusual physical implications.)

 

[PeterDonis]

And now that I look at the "talk page" for the Wikipedia article

Once again, I would not consider Wikipedia, particularly a talk page, to be a good source of information for something like this.

there may be additional states of matter beyond neutron/quark densities but less than the infinities of a singularity.

AFAIK this is a sort of "Hail Mary pass" speculation by people who don't want to accept the straightforward implications of classical GR regarding the formation of event horizons.

Basically the problem is this: to have a stable static equilibrium "end state" of matter that will resist gravitational collapse indefinitely, it needs to be stable at zero temperature, because otherwise it will radiate away energy and become more tightly bound. (Yes, technically it only needs to be stable at the temperature of the CMBR, but that's effectively zero temperature for this problem.) Also it needs to be made of fermions, because at zero temperature the only possible source of pressure is fermion degeneracy pressure (the Pauli exclusion principle)*. And it needs to be made of particles that don't decay into other particles, because otherwise they will, giving off energy and making the system more tightly bound.

[* - Edit: Technically the strong nuclear force is believed to become repulsive at short distances, so it does provide some pressure in neutron stars. AFAIK this only happens if quarks are involved; an object made solely of gluons, like a glueball, would not, AFAIK, exhibit this behavior. In any case, what I say below about the maximum mass limit applies even if a short-range repulsive interaction provides some pressure in addition to fermion degeneracy.]

The list of known particles out of which you can make a stable object that meets the above criteria is very short: electrons, up quarks, and down quarks. Electrons make white dwarfs; up and down quarks make neutron stars. And we know that both of those types of objects have a maximum mass limit; for white dwarfs it's 1.4 solar masses, for neutron stars it's around 1.5 to 3 solar masses (AFAIK, I haven't seen a recent estimate). Furthermore, the theoretical reasons why these objects have a maximum mass limit (basically because there is a relativistic limit to the ratio of pressure to density) would seem to be applicable to *any* object made out of fermions that meets the above criteria; so even if we discover some other stable fermions, stable objects made out of them should have a maximum mass limit as well.

I think it's strange that most articles on black holes never mention that the idea of a singularity is just a theory and that what actually happens when mass collapses into itself is completely unknown.

They don't say this because it isn't true. Classically we *do* know what actually happens when mass collapses into itself. We don't know the full effects of quantum corrections, as I said before, but we still know quite a lot, so to say that it's "just a theory" and what actually happens is "completely unknown" is a serious misstatement.

 

[Mordred]

I read that article, it was interesting so I will probably examine again in more detail.

I just come across this paper on Kerr Schild geometry, they make some interesting claims in it.
http://arxiv.org/abs/1212.5595

It goes into BHs with no event horizon I'm still reading it but as its related thought I would post it.

 

[photonkid]

Classically we *do* know what actually happens when mass collapses into itself.

If we did know what actually happens, you wouldn't qualify with "classically". Roy Kerr told me we don't know what happens inside a "black hole" (whatever he meant by "black hole") and I believe him.

 

[PeterDonis]

If we did know what actually happens, you wouldn't qualify with "classically".

If we knew nothing at all about what actually happens, I wouldn't have made the statement even with the qualification.

Roy Kerr told me we don't know what happens inside a "black hole" (whatever he meant by "black hole")

Exactly: "whatever he meant". Do you know what he meant? Do you think he meant that horizons don't form? Or do you think he meant that we can't see what happens inside horizons (by definition), so we can't have direct knowledge of what happens there? I think he meant the latter.

 

[Nugatory]

Roy Kerr told me we don't know what happens inside a "black hole" (whatever he meant by "black hole") and I believe him.

That's a different and much more reasonable claim than the claim that infalling objects don't cross the event horizon within a finite amount of proper time.

We really don't know what happens on the far side of the event horizon predicted by the Schwarzschild solution. We do know what GR predicts, and we have no particular reason to doubt those predictions except in the immediate vicinity of the central singularity; but we don't know that those predictions are correct.

 

[PeterDonis]

When it comes to the Schwarzschild solution an observer passing the event horizon is A-OK 'because the math shows it', but when we start talking about a Kerr solution and an observer goes into the ergosphere or beyond it is suddenly 'obviously' no longer physical.

The two cases are different because what the math shows is different. In the Schwarzschild solution, the math shows a horizon forming; that's all. In the case of the Kerr interior, the math shows closed timelike curves forming inside the inner horizon. (I have never seen a reputable physicist claim that the ergosphere, which is outside the outer horizon, is "obviously no longer physical"; indeed, a good portion of writing about the ergosphere specifically discusses how to use it to extract energy from a rotating black hole. The only claims I've seen about a portion of the Kerr spacetime being "unphysical" refer to the region inside the inner horizon where CTCs are predicted.)

It's worth noting, also, that physicists' beliefs about what happens in gravitational collapse are not just based on the limited number of exact solutions we know, since obviously those have a high degree of symmetry and a realistic collapse would not. A realistic model of a collapse should be stable against small perturbations, and none of the highly symmetric exact solutions are AFAIK. The only exact solution for a collapse that I'm aware of that is stable against small perturbations is the BKL model, which seems to be the current "best guess" at an exact solution for the region far inside the horizon in a realistic collapse.

Also, numerical simulations have been done of a lot of non-symmetric collapse scenarios, and AFAIK all of them show horizons forming. I don't know if any of the simulations of rotating collapses have shown any regions corresponding to the Kerr interior, but I suspect not since the Kerr interior is not stable against small perturbations.

 

[photonkid]

If we knew nothing at all about what actually happens, I wouldn't have made the statement even with the qualification.

But if physicists are still debating whether event horizons actually exist, how can you say we know what actually happens?

Exactly: "whatever he meant". Do you know what he meant? Do you think he meant that horizons don't form? Or do you think he meant that we can't see what happens inside horizons (by definition), so we can't have direct knowledge of what happens there? I think he meant the latter.

I will ask him after I do some more reading.

I'm not a physicist and it's hard for me to grasp these arguments about "proper time" continuing for an object falling into a black hole. How could mass that falls past the event horizon ever make it to the singularity in "our time"?

If the mass of the Earth became a black hole, it would have an event horizon radius of 1 cm or something. So photons coming from the sun should reach the center of the black hole real fast (in our time). If it was possible to measure it, would we see the photon slowing down inside the event horizon?

Does light slow down in "our time" when it "goes past" a large mass?

 

[Passionflower]

The only claims I've seen about a portion of the Kerr spacetime being "unphysical" refer to the region inside the inner horizon where CTCs are predicted.)

I just love to have a pair of batteries with negative energy, then I can finally get my anti-gravity rockets to work.

By the way I really do not see the big deal about CTC's, so the state of an object keeps rotating: "rock, paper, scissors", rendezvous-ing allover again, so what?

 

[photonkid]

I just love to have a pair of batteries with negative energy, then I can finally get my anti-gravity rockets to work.

http://www.stuff.co.nz/the-press/christchurch-life/8372542/Bright-sparks-and-black-holes

<quote> He says there is this little idea he has about negative particles that would have repulsive gravity. If he can refine the mathematical detail, he might just alarm his hosts with a presentation when he collects his Einstein Medal in May. </>

 

[pervect]

And now that I look at the "talk page" for the Wikipedia article,

The Wiki isn't a terribly reliable source. The talk page is probably slightly less reliable than the wiki.

I think it's strange that most articles on black holes never mention that the idea of a singularity is just a theory and that what actually happens when mass collapses into itself is completely unknown.

This is a bit of a non-sequitur. The central singularity is not the event horizon.

I don't really agree with the remarks made about the singularity either but that seems like a topic for a different thread.

Sticking to the topic of the event horizon and not getting sidetracked:

The event horizon is both predicted by GR, and confirmed well by experiment. One recent paper:

http://arxiv.org/abs/0903.1105

Black hole event horizons, causally separating the external universe from compact regions of spacetime, are one of the most exotic predictions of General Relativity (GR). Until recently, their compact size has prevented efforts to study them directly. Here we show that recent millimeter and infrared observations of Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, all but requires the existence of a horizon. Specifically, we show that these observations limit the luminosity of any putative visible compact emitting region to below 0.4% of Sgr A*'s accretion luminosity. Equivalently, this requires the efficiency of converting the gravitational binding energy liberated during accretion into radiation and kinetic outflows to be greater than 99.6%, considerably larger than those implicated in Sgr A*, and therefore inconsistent with the existence of such a visible region. Finally, since we are able to frame this argument entirely in terms of observable quantities, our results apply to all geometric theories of gravity that admit stationary solutions, including the commonly discussed f(R) class of theories.

The short version of this is that our black hole candidate is -- black. If it were any sort of object with an observable surface, we'd expect to see radiative emissions from said surface due to infalling matter. For instance, we can easily detect the surface of a neutron star if matter is falling on it.

The primary astrophysical importance of a horizon is
that the gravitational binding energy liberated by ma-
terial as it accretes can be advected into the black hole
without any further observational consequence. This is
very different from accretion onto other compact objects,
e.g., neutron stars, in which this liberated energy ulti-
mately must be emitted by the stellar surface.

There may still be a few small experimental loopholes, but the bulk of the evidence very storngly suggests that event horizons are very real, and that Sag. A has an event horizon.

Event horizons are also firm theoretical predictions of SR.

The fact that one can reach the event horizon in a finite proper time is another firm theoretical prediction of GR.

 

[PeterDonis]

But if physicists are still debating whether event horizons actually exist, how can you say we know what actually happens?

I didn't say we know what actually happens, period. I said we know a lot more than nothing. We know that classically a horizon is predicted to form. We know that quantum effects, if they are going to prevent the horizon from forming, would have to be large: just small changes in the classical behavior won't do it. And we know that, for black holes of astronomical size, the spacetime curvature at the horizon is small compared to the expected scale of quantum gravity (which would be a radius of curvature comparable to the Planck length); it's hard to see how quantum corrections could be large in such a regime.

As I understand it, arguments like these are why the current mainstream view is that horizons form. (AFAIK arguments like Susskind's for why this does not violate quantum unitarity are also mainstream, but that's really a separate question since it has to do with how quantum corrections affect the singularity as well as the horizon.)

Btw, it's important to distinguish two things: whether or not a horizon forms, and whether or not a singularity forms (meaning a singularity at r = 0, the "center" of the black hole). All the stuff I said above (and in earlier posts) was about whether or not a horizon forms. But even if a horizon forms (because quantum corrections are too small to prevent it for a black hole of astronomical size), we still expect quantum corrections to the classical behavior to be large as the singularity is approached, because the classical prediction is that spacetime curvature increases without bound in that regime, so at some point it will certainly reach the Planck regime.

I'm not a physicist and it's hard for me to grasp these arguments about "proper time" continuing for an object falling into a black hole. How could mass that falls past the event horizon ever make it to the singularity in "our time"?

The classical prediction is made using the same sort of math that predicts a finite proper time to fall to the horizon. However, the use of the term "our time" is not correct. The coordinates that are "natural" to an observer far away from the black hole, which are where the concept of "our time" comes from, simply do not cover the region of spacetime inside the horizon. Many people get hung up over this because they simply can't conceive how that can be; but once again, the math is unambiguous, and it is not controversial at all.

If it was possible to measure it, would we see the photon slowing down inside the event horizon?

This question doesn't really have a meaningful answer, because there's no way to define what "slowing down" means inside the horizon. Outside the horizon, there is a set of "hovering" observers that stay at the same altitude above the horizon, and these observers can be used as a reference to define what "time slowing down" means (observers closer to the horizon have clocks that "run slow" compared to observers higher up). Inside the horizon, there are no such observers, so there's no way to construct a reference for "time" that works the way the reference system outside the horizon does.

(This lack of "hovering" observers inside the horizon is related to the fact I noted above, that the natural time coordinate in the exterior region does not cover the interior region.)

Does light slow down in "our time" when it "goes past" a large mass?

If you mean light that stays outside the horizon (including the case where the mass doesn't have a horizon, like an ordinary planet or star), then yes (where "slow down" means relative to the time reference I described above, that only works outside the horizon). This is called the Shapiro time delay, and it has been measured:

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

 

[photonkid]

The Wiki isn't a terribly reliable source. The talk page is probably slightly less reliable than the wiki.

So is there any detail on this page that you dispute and if so, why don't you correct it? It seems to me that the people contributing to the article are mainstream physicists and considering the unpleasantness and number of kooks on the usenet relativity forum, it's just as well.

The short version of this is that our black hole candidate is -- black. If it were any sort of object with an observable surface, we'd expect to see radiative emissions from said surface due to infalling matter. For instance, we can easily detect the surface of a neutron star if matter is falling on it.

But does time slow down close to the neutron star as it does close to the "almost" event horizon of an almost black hole.

The fact that one can reach the event horizon in a finite proper time is another firm theoretical prediction of GR.

You mean in the falling object's frame of reference? Can the falling object reach the singularity? The closer you get to the singularity, the slower time goes?

 

[photonkid]

As I understand it, arguments like these are why the current mainstream view is that horizons form. (AFAIK arguments like Susskind's for why this does not violate quantum unitarity are also mainstream, but that's really a separate question since it has to do with how quantum corrections affect the singularity as well as the horizon.)

Btw, it's important to distinguish two things: whether or not a horizon forms, and whether or not a singularity forms (meaning a singularity at r = 0, the "center" of the black hole). All the stuff I said above (and in earlier posts) was about whether or not a horizon forms. But even if a horizon forms (because quantum corrections are too small to prevent it for a black hole of astronomical size), we still expect quantum corrections to the classical behavior to be large as the singularity is approached, because the classical prediction is that spacetime curvature increases without bound in that regime, so at some point it will certainly reach the Planck regime.

ok, so this page
http://en.wikipedia.org/wiki/Black_hole#Singularity
says <quote> there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities. </>
Do you know if this is a correct statement?

Many people get hung up over this because they simply can't conceive how that can be; but once again, the math is unambiguous, and it is not controversial at all.

(This lack of "hovering" observers inside the horizon is related to the fact I noted above, that the natural time coordinate in the exterior region does not cover the interior region.)

ok, I haven't managed to understand special relativity yet so I'm not likely to understand this in the near future.

If you mean light that stays outside the horizon (including the case where the mass doesn't have a horizon, like an ordinary planet or star), then yes (where "slow down" means relative to the time reference I described above, that only works outside the horizon). This is called the Shapiro time delay, and it has been measured:

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

Yes, that's what I meant. Thanks.

 

[photonkid]

If you DO like my suggested definition, hopefully I have already answered your question, and you just neeed to read it and think it over a bit.

Well for your information, your answer comes across as arrogant and convoluted. Nobody else in this thread saw any need to debate what "exists" means.

Also, note that although the subject was "does an event horizon ever exist", in the content I said
<quote> Is it true that the event horizon never comes into existence - or at least, if time slows down like general relativity suggests, would an event horizon and a singularity never come into existence? </>

If you wanted me to take your answer seriously you should have said
"mainstream physicists believe that event horizons actually do exist because..."

"mainstream physicists do/ do-not believe that singularities exist because..."

since it turns out that the answer is quite complicated evidenced by the fact that people in this thread are debating what happens to time near an event horizon.

 

[PeterDonis]

<quote> there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities. </>
Do you know if this is a correct statement?

AFAIK it is, yes. I note that there is a statement later on on that Wiki page, in the "Alternatives" section, to the effect that a quantum gravity will not feature any event horizons either. I wasn't aware that that was a mainstream view (as I've said in this thread), but the footnote there references a review article in Annalen der Physik that I haven't read. I'll take a look at it.

 

[Nugatory]

But does time slow down close to the neutron star as it does close to the "almost" event horizon of an almost black hole.

Yes. Also close to the surface of the earth, although there the effect is much smaller because the gravitational field of the Earth is much weaker than that of a neutron star. It's been measured on Earth.

 

[Nugatory]

So is there any detail on this page that you dispute and if so, why don't you correct it?

Editing some wikipedia pages is a thankless and Sisyphean task.
Answering questions here is merely thankless.

 

[Nugatory]

The fact that one can reach the event horizon in a finite proper time is another firm theoretical prediction of GR.

You mean in the falling object's frame of reference?

(Be aware that "frame of reference" is a treacherous concept in GR; usually you're better off thinking in terms of local inertial frames)

Pervect specifically said "proper time"; proper time is frame-independent. Intuitively, proper time is the amount of time that passes for a single clock that travels on some path between two points in space-time. It is the same for all observers and is in no way affected by changing frames of reference.

For example, if my airplane takes off at noon according to my wristwatch and lands at 1:00 according to that same wristwatch, all observers everywhere will agree about three facts: the watch read noon at takeoff; the watch read 1:00 at landing; I experienced a one-hour journey and aged one hour between takeoff and landing. Thanks to time dilation, relativity of simultaneity, and other relativistic effects, the observers may have measured very different times for my journey, but they all agree that for me it was a one-hour journey. That's proper time.

It's important to understand that proper time only works for a single clock that's only at a single place at any moment. My wristwatch measures the proper time that I experience, but it tells me nothing about the experience of other observers outside the airplane.

Can the falling object reach the singularity?

Yes, in a finite amount of proper time according to classical GR - see #12 in this thread. It is likely that classical GR stops working very close to the singularity, in which case the answer might be different... but if so, that happens long after the infalling object has passed through the event horizon.

 

[PeterDonis]

I note that there is a statement later on on that Wiki page, in the "Alternatives" section, to the effect that a quantum gravity will not feature any event horizons either. I wasn't aware that that was a mainstream view (as I've said in this thread), but the footnote there references a review article in Annalen der Physik that I haven't read. I'll take a look at it.

Having looked at it, I don't see anything in that article that says that quantum corrections are expected to prevent a horizon from forming. I do see references to the fact that, in order to show unitarity, you have to include amplitudes for spacetime histories where a black hole does not form, as well as for histories where one does form. But it also says that macroscopic black holes have classical behavior that emerges from the underlying quantum amplitudes in the same way as for any other macroscopic object, and that classical behavior includes a horizon.

So I'm sticking with what I said earlier in this thread: it looks like the mainstream physics view is that quantum corrections will remove the singularity, but not the event horizon.

 

[photonkid]

So I'm sticking with what I said earlier in this thread: it looks like the mainstream physics view is that quantum corrections will remove the singularity, but not the event horizon.

ok, well having re-read most of this entire thread including what you said here it's hard for me to understand how an outside observer will see a falling object frozen indefinitely at the edge of the event horizon yet the object does actually reach the event horizon. It seems that this is not analogous to trying to accelerate an object of non zero mass to the speed of light. It also seems that the evidence that black holes do actually exist is strong and mainstream physics view is that event horizons are most likely real.

I suggest you don't try to explain any further but do you know if there are any authoritative articles or books that explain what happens when a star collapses e.g. that the event horizon starts out very small and gets gradually bigger or whatever happens, and why an object is frozen indefinitely at the edge of the event horizon from an outside observer's view?

Anyway, thanks for the considerable time you've spent posting in this thread, and everyone elses.

 

[PAllen]

An authoritative description of collapse including the evolution of the event horizon is the following:

http://www.aei.mpg.de/~rezzolla/lnotes/mondragone/collapse.pdf

As they discuss, the event horizon grows from the center of collapsing body, and stop growing as all the mass is encompassed.

As for what a distant observer sees for, e.g., a rod falling through a horizon, see if this helps:

- light emitted at one millimeter (say) above the horizon is received eventually as long microwaves.
- light emitted at 1/2 millimeter is received as radio waves.
- light emitted at .1 millimeter above the horizon is so long wave that no plausible detector can detect it (even ignoring being swamped by CMP radiation).

So, what you actually see is the rod getting redder and redder (including radio waves in this), finally the front disappears at radius of last detectability. Then further up the rod disappears as it reached this radius; etc. until the whole rod has disappeared. This process will actually happen relatively fast for the distant observer, despite the extreme time dilation of the near horizon region relative to the distant region. Visually, with our ideal detector, it looks for all the world like the rod has progressively vanished into a black hole in space.

 

[photonkid]

As for what a distant observer sees for, e.g., a rod falling through a horizon, see if this helps:

Thanks. It helped from the point of view that now I know what "pancaked" means. Also it helped that I no longer think the in-falling object remains visible to an outside observer indefinitely, but... at first glance my brain is still seeing a paradox because
1. it sounds like the wavelength coming from the in-falling observer approaches infinity and that to an outside observer, the wave never stops coming
and
2. the closer the in-falling object gets to the event horizon, the slower time goes, so he never quite makes it - just like trying to reach the speed of light

But for 1, it probably does stop coming because after a certain time, you have to wait an infinite amount of time to see any more "oscillations in the wave". For 2, it's impossible for me to come up with any kind of numbers that show no matter how close you get you never quite make it because the external observer can't see what's happening, whereas for accelerating to the speed of light, the object being accelerated can do the measuring and no external observer is needed.

So if it's a paradox, it's a very complicated paradox and I can't actually tell if there's a paradox or not...

Anyway, I've been wondering why this isn't in an FAQ somewhere and then today I found that it's here
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html


Is there any possibility that when a star collapses, that time slows down so much that the density of the mass never goes past a certain limit and that even though the star keeps on contracting, the contraction rate gets smaller and smaller? Does the maths show this can't happen - or is it because this would look like a neutron star and black hole candidates don't look like neutron stars? (A short answer will do).

 

[PeterDonis]

Is there any possibility that when a star collapses, that time slows down so much that the density of the mass never goes past a certain limit and that even though the star keeps on contracting, the contraction rate gets smaller and smaller?

No.

Does the maths show this can't happen

Yes. This case is treated in all of the major relativity textbooks.

or is it because this would look like a neutron star and black hole candidates don't look like neutron stars?

Sort of. There is a theorem (originally due to Einstein) that says that an object in a static equilibrium, like a neutron star (or a white dwarf or anything else that holds itself up statically against its own gravity) can't have a radius smaller than 9/8 of the Schwarzschild radius for its mass. The time dilation factor at that radius is only 3 (i.e., time at the surface of such an object "flows" 1/3 as fast as it does at infinity); it certainly isn't approaching infinity.

One of the key things about black hole candidates is that at least some of them appear to be confined within a radius smaller than the above limit. (At least, that's my understanding.) So whatever is in there, it can't be something in static equilibrium like a neutron star.

 

[A.T.]

There is a theorem (originally due to Einstein) that says that an object in a static equilibrium, like a neutron star (or a white dwarf or anything else that holds itself up statically against its own gravity) can't have a radius smaller than 9/8 of the Schwarzschild radius for its mass. The time dilation factor at that radius is only 3 (i.e., time at the surface of such an object "flows" 1/3 as fast as it does at infinity); it certainly isn't approaching infinity.

What about the time dilation at the center of such an object?

 

[PeterDonis]

What about the time dilation at the center of such an object?

It depends on the object's internal structure, but it will in general be somewhat larger than at the surface. It can't go to infinity because the gradient of the time dilation factor gets smaller as you go inward from the surface, until it becomes zero at the center.

 

[photonkid]

Sort of. There is a theorem (originally due to Einstein) that says that an object in a static equilibrium, like a neutron star (or a white dwarf or anything else that holds itself up statically against its own gravity) can't have a radius smaller than 9/8 of the Schwarzschild radius for its mass. The time dilation factor at that radius is only 3 (i.e., time at the surface of such an object "flows" 1/3 as fast as it does at infinity); it certainly isn't approaching infinity.

So when we hear about the age of the universe being 13 billion years, is that 13 billion years of "earth proper time"? Since planet Earth hasn't been around all that time, where does "13 billion years" come from - is it 13 billion years of "zero gravity/ zero velocity" time?

13 billion years is presumably long enough for a black hole to form. Is it possible to calculate how long it would take (in Earth years) for an infalling object to fall the last one meter before it reaches the event horizon and if so, is this likely to be longer than 13 billion "earth years". Hopefully you can see what I'm trying to get at.

 

[PeterDonis]

So when we hear about the age of the universe being 13 billion years, is that 13 billion years of "earth proper time"?

Not really. It's the proper time that would be elapsed since the Big Bang for an observer whose current spatial location is Earth, but who has always seen the universe as homogeneous and isotropic. Such observers are called "comoving" observers. We don't see the universe as isotropic on Earth: we see a dipole anisotropy in the CMBR, for example, indicating that we are not "comoving" observers, even when the effects of the Earth's rotation and orbit about the Sun are corrected for.

13 billion years is presumably long enough for a black hole to form.

Way more than enough, yes.

Is it possible to calculate how long it would take (in Earth years) for an infalling object to fall the last one meter before it reaches the event horizon

Yes.

is this likely to be longer than 13 billion "earth years".

It's a lot shorter, even for the largest black holes that we think are likely to exist in the universe (the current estimate, I believe, is black holes of billions of solar masses at the centers of quasars). For a black hole of that size, the time for an infalling object to fall the last one meter to the horizon is much less than one Earth year. Even the time to fall from an astronomically significant distance, such as a million light-years (i.e., from well outside the quasar the black hole is at the center of), is less than 13 billion years.

Note that the "time" I'm referring to here is the proper time experienced by the infalling object, i.e., the time elapsed on that object's clock.