Yes, of course in the frame of the infalling matter, it reaches the event horizon and indeed reaches the singularity in a finite time. I’m not fully understanding your objection – are you just unable to accept that different observers experience different proper times between two events? If a person holding a clock falls into a black hole, he will of course see his clock ticking normally. According to General Relativity, an external observer would see the clock slow down more and more as it approaches the horizon. Do you accept that?
Of course. I’m not arguing against the different frames of reference. I’m arguing against what I interpreted – perhaps incorrectly – to be your implication that matter can never actually fall into a black hole. If that were true, singularities and black holes as we understand them could never form in the first place. But certainly the predominant scientific consensus is that it can, and they do.
This is as good an article as I’ve found trying to explain this apparent paradox. The key quote:
If we program a space probe to fall freely until reaching some randomly selected point outside the horizon and then accelerate back out along a symmetrical outward path, there is no finite limit on how far into the future the probe might return. This sometimes strikes people as paradoxical, because it implies that the in-falling probe must, in some sense, pass through all of external time before crossing the horizon, and in fact it does, if by “time” we mean the extrapolated surfaces of simultaneity for an external observer. However, those surfaces are not well-behaved in the vicinity of a black hole. It’s helpful to look at a drawing like this.
This illustrates schematically how the analytically continued surfaces of simultaneity for external observers are arranged outside the event horizon of a black hole, and how the in-falling object’s worldline crosses (intersects with) every timeslice of the outside world prior to entering a region beyond the last outside timeslice. The timeslices have the form
[INDENT]tj − T = 2m ln(r/2m − 1)
where T is the (inward) Eddington-Finkelstein time coordinate. We just repeat this same shape, shifted vertically, up to infinity. Notice that all of these infinitely many time slices curve down and approach the same asymptote on the left. To get to the “last timeslice” an object must go infinitely far in the vertical direction, but only finitely far in the horizontal (leftward) direction.
The key point is that if an object goes to the left, it crosses every single one of the analytically continued timeslice of the outside observers, all the way to their future infinity. Hence those distant observers can always regard the object as not quite reaching the event horizon (the vertical boundary on the left side of this schematic). At any one of those slices the object could, in principle, reverse course and climb back out to the outside observers, which it would reach some time between now and future infinity. However, this doesn’t mean that the object can never cross the event horizon. It simply means that its worldline is present in every one of the outside timeslices. In the direction it is traveling, those time slices are compressed infinitely close together, so the in-falling object can get through them all in finite proper time (i.e., its own local time along the worldline falling to the left in the above schematic).[/INDENT]
Another quite interesting intuitive explanation from the same site is found here. Interpreted strictly in terms of Schwarzchild coordinates, one can regard an infalling object as taking infinitely long to pass the event horizon, and then (recalling what happens to the time dimension beyond the EH in the Schwarzchild solution) traveling back in time to the present in Schwarzchild coordinate time as it progresses from the EH to the singularity, yielding a net transit time to the inevitable singularity as seen by an external observer to be not much different from its own proper time. I have no idea if this interpretation makes physical sense, but not much beyond the event horizon really does. If we launch a massive object into a black hole and very soon observe that the radius of its event horizon has grown, then something like this must be true.
That’s not just tangential, it’s actually extremely relevant to the above conversation. Perhaps more knowledgeable posters than I will want to comment, but ISTM that if the interpretation is correct and this is what they think it is – namely that a dying star well beyond the Chandrasekhar limit has suddenly disappeared – then it’s proof positive that matter can be observed to fall into a black hole in a short time from a frame of reference at an effectively infinite distance outside the gravity well. The only way a massive collapsing star can suddenly disappear is if it is engulfed by its own event horizon.
The easiest way to see is from a Penrose diagram like the below:
We can ignore the bottom (white hole interior) and left (parallel universe) regions of the diagram(s) as they are features of the extended solution.
In a Penrose diagram light always has worldlines at 45 degree angles to the vertical axis, and the worldlines of objects moving at less than the speed of light are always at an angle that is less than 45 degrees to the vertical axis.
It should be easy to see that nowhere on the BH singularity (upper zig-zag) is causally connected to the whole of the BH exterior region (right region), which means an observer hitting the singularity cannot see the entire future of the Universe played out before they hit the singularity.
The misapprehension that you are able see the entire future of the Universe before you hit the singularity comes from taking Schwarzschild coordinates (the dotted lines in the BH exterior region. NB as illustrated the lines do not mark out equal amounts of coordinate time or distance) too literally. Schwarzschild coordinates map all the events that lie on the event horizon to the same time coordinate* as timelike future infinity (i[sup]+[/sup]), to which all events in BH exterior region are causally connected and in the past (therefore if you make it to i[sup]+[/sup] you are able to see every event that happened in the BH exterior region).
*Strictly speaking they don’t because the Schwarzschild time coordinate goes to infinity at both the event horizon and at i[sup]+[/sup], so the problem is more from making faulty assumptions by incorrectly taking limits when the coordinates are singular.
Is there a way to easily explain the difference between the singularity at the center of a very massive black hole versus the singularity at the center of a small black hole? If both are considered infinitely dense, how is there a difference between them?
It occurred to me; a giant star with a diameter of dozens of AUs…several lighthours…due to causality, the center of the star’s core collapsing to singularity would not cause any immediate noticeable effect on the star’s surface. I can imagine as the effect reaches the surface, the star would indeed wink out…unless the star is rotating, creating an accretion disk.:rolleyes:
BTW…instead of an infinitesimal geometric point possesing infinite density, a singularity of one planck mass per cubic planck distance would create a non-“divide by zero” situation.
It also occurred to me, instead of a 3D tiny object, it could be a 4D object as per General Relativity, 11D as per M-Theory, 26D as per Bosonic String theory, or even a 248D as per Exceptionally Simple theory of Everything.
I don’t think that really proves your point. As the matter falls into the hole, its time slows down from our perspective. It emits (more and more red-shifted) photons at a slower and slower rate, until the rate of photon emission becomes so slow that it effectively stops radiating, from an external perspective. The matter seems to have disappeared, but it’s still emitting photons at a rate too slow to be easily detectible.
That’s a peculiar definition of “still emitting photons”. At a very short time after the object crosses the event horizon, the last photon from it will be received. No other photons, no matter how redshifted, will ever come out.
Well, no photons or information specifically tied to that particular object that fell in. There’s still predicted to be Hawking radiation, though as I understand the mechanism that starts off as particles, even though they annihilate and become photons nearly immediately. Photons are predicted to be emitted from the area of the black hole, at any rate.
Except that as per several different takes at intuitive explanations that were provided upthread, this is due to an incomplete interpretation of infalling objects only as seen in the Schwarzchild coordinates in which the event horizon appears to be a singularity, but it’s only a coordinate singularity and not a physical one. If this was a complete interpretation, then as already noted no objects could ever fall into a black hole and black holes could never form.
Hawking radiation is unrelated to infalling ordinary matter, which AFAIK is believed to typically produce X-rays and gamma rays due to the extreme forces of tidal effects. Hawking radiation is usually described as being related to the black hole’s interaction with the quantum vacuum – with the absorption of one of the partners of the virtual particle pairs constantly appearing in the vacuum, and removing it from the universe before it can annihilate its partner.
To continue my quibble, Hawking radiation is related to the mass of the black hole, which in turn is related to the amount of mass that has fallen in. As you add mass the amount of energy released per unit time will decrease, though of course over the truly long term the energy released before the hole evaporates will go up.
It’s not due to tidal effects. Very large black holes, such as those found in the centers of galaxies, have very small tidal effects at the horizon, and yet still often cause infalling matter to release prodigious amounts of energy. Mostly, it’s just due to the fact that the vicinity of a black hole is often quite crowded.
Yes, that’s more or less true, and thank you for the correction as it was wrong for me to imply that tidal effects are the sole cause of what are actually very complex phenomena.
However I would ask whether you don’t agree it’s true that tidal effects (i.e.- the amount of gravitational gradient near the EH), black hole rotation, and mass accretion rate are among the factors governing the behavior of the visible phenomena produced by infalling objects, like accretion disks and jets of ejected matter and energetic radiation.
For example, even for supermassive black holes, tidal effects are significant if the object in question is large enough, like a nearby star, leading to tidal disruption events that shred the star into an accretion disk. It’s been suggested that a star falling into a sufficiently large ultramassive black hole might disappear with much less visible effect. By the same token, a much smaller object that was small relative to the gravitational gradient of the BH might fall through the EH more or less intact. I think perhaps the key here is that in such cases, most of the energy of the object’s gravitational potential would vanish beyond the event horizon and would never be seen.
Perhaps somewhat nitpicky points, but I’m just suggesting that the gravitational gradient isn’t by any means irrelevant, though you’re absolutely right that it’s not usually the primary cause of X-ray or gamma ray emission.
Yeah, tidal effects can shred stars into an accretion disk, but there are a lot of other effects that can give you an accretion disk, too. I suspect that, for a supermassive black hole, dynamical friction is the dominant one, though I’m not certain on that.
TBH I don’t think it is entirely known what causes the emissions from quasars, though it is undoubtedly related to accretion. It has been suggested a significant portion of the emission may be related to the Penrose effect, which is the classical limit of Hawking radiation.
You mean, that the accretion is spinning down the black hole? I’ve never heard that one. Wouldn’t that require that the hole and its accretion disk somehow form with opposing angular momentum?
You’re right in that the bog-standard kinematic Penrose effect is not really a feasible way (I believe) for a black hole to actually be radiating energy, the proposed method is the Blandford–Znajek process.
