On the nature of the "infinite" fall toward the EH

PAllen

Yes it would. Unfortunately, the correct answer is not known. Somewhere in this thread I posted links to a 2007 paper by Krauss et.al. that argues one position; and a paper by Padmanabhan et.al. from 2009 that claims to refute the former. My belief is that the 2009 paper represents the 'majority view' (and I can't find any response to it from the 2007 authors), but it is far from 'settled physics'. Without responding to the 2009 paper, there are certainly new papers written in the framework of the 2007 paper. It appears to me that both string theory and LQG are more consistent with the framework of the 2009 paper, as is Hawking's proposal for resolving the information paradox.

PAllen

I don't agree. I think this will be forced only if e1 and e2 are too far apart (or if you try to include too much outside the region defined by two ingoing null paths, Lucky world line, and the singularity). That is, there is a global prohibition, but not quasi-local problem.

Think of the Kruskal chart, and singularity region in the right half (that matches the GP singularity ordering). Specifically, to make it easy, think of a two singularity arrival events that are nearly horizontal in the chart, and close together, and connect them out with light paths to some static, radial, external world line. Now, within this sliver, we just change all simultaneity surfaces by one degree from horizontal, counterclockwise.

[Edit: Actually, K-S shows a stronger result. It is global, and reverses GP singluarity arrival ordering for 'half' the singularity arrival events. It seems to me, that distortions of K-S can reverse GP ordering in a consistent global chart for all singularity arrival events before (in GP sense) any chosen one. What you can't do is accomplish this for the whole singularity arrival sequence.]

PeterDonis

I see what you mean, but I'm not sure the time ordering on the singularity will be monotonic if you do this. I don't really trust my powers of visualization for this, so I'll have to think about it some more to see if I can come up with a mathematical way to tackle it.

PAllen

Just consider the simple transform (producing ugly metric):

V' = V - k U
U' = U

using the conventions where V is the K-S time coordinate, -1 < k < 1. Lines of constant V' are spacelike everywhere; lines of constant U' are the same as lines of constant U. While the metric gets ugly, it is not hard to see that increasing k towards 1 shifts the inflection in singularity ordering as far to the right as desired; decreasing k towards -1 shifts the inlection to the left. So, for any two events on the singularity, you can get an ordering where the left is first for some k close to -1, and where the right is first for some k close to 1. Each of these charts is global, with the same time ordering for causal curves as the original K-S chart.

This fully justifies (better late than never) my original statement that for any two light signals reaching the singularity from Lucky, Lucky can consider the arrival events to be the reverse of the emission events. The only thing Lucky can't do is achieve such an inversion over the whole history of a static world line. It can be achieved for any segment of interest, but not for the whole past/future eternal history.

Also, note that none of this contradicts Dalespam's improved wording: If light from e1 reaches Unlucky as Unlucky reaches the singularity, light from any event e2, later on Lucky's world line, will not reach Unlucky at all. This wording is coordinate independent. Wording on the order of the two singularity arrival events is coordinate dependent (as expected by the spacelike relation between them).

A final observation is that Lucky can achieve total time order on the singularity consistent with their world line time order using a variety of coordinates (Lemaitre, GP, EF, etc.). A mirror Lucky in region III would use a mirror version of each these coordinate systems to achieve a total singularity ordering consistent with their world line.

PeterDonis

Yes, but there will always *be* an inflection point; you can never produce a completely monotonic ordering on the singularity this way. That's all I am saying; that a *monotonic* ordering on the singularity can't be reversed without also reversing the time ordering of events on timelike curves (unless you restrict attention only to portions of timelike curves inside the horizon). No K-S style chart gives a monotonic ordering.

Only if he's willing to accept a non-monotonic ordering of events on the singularity. The emission events are outside the horizon, so there's no way to obtain a reversed monotonic ordering of all events on the singularity that keeps the ordering of emission events the same. If you only want to reverse the arrival events, but allow the complete ordering to be non-monotonic, then yes, you can always do that, as you have shown.

Yes, agreed.

Yes, and once he's done this, he can't reverse that order while still keeping the ordering the same on his own worldline. (In fact, he can't even reverse it and still *cover* his own worldline; see below.)

Yes, but any such coordinate chart won't cover region I at all. So Lucky and mirror Lucky can never have a common chart that (1) covers both of their worldlines, and (2) agrees on a monotonic ordering of events on the singularity.

PAllen

Except possibly as a brief, initial speculation, corrected almost immediately, I never claimed monotonic was possible. After backing off from that, everything else I thought turned out to be justified; much more than just a chart bounded e1 to e2 on Lucky's world line, light rays to the singularity, and the singularity arrival events - that reverses arrival order relative to transmission order. Instead, the whole of the K-S manifold can be covered, reversing e1 and e2 arrival; all that can't be done is to reverse the entire singularity arrival ordering.

PAllen

Yes, I completely understand this. I don't think I suggested otherwise.

PeterDonis

Yes, I agree, you didn't. I was only trying to make the point that, even though the singularity is spacelike, there *is* a possible monotonic "time ordering" of events on the singularity, which matches the time ordering of events on Lucky's worldline. That's kind of counterintuitive for a spacelike surface.

Mike Holland

OK, but I was thinking of observers taking into account any motion relative to the black hole or any local gravity fields, and using SR and GR to calculate its effects on their observations. I thought they would be left with a time dilation which would be the same for all distant observers observing the same clock near the same supermassive object. They should see what O-S calculated for their ideal case.

PAllen, I obviously need to read up on close orbiting neutron stars, but what does SOL mean?

PeterDonis

But any such "effects" will be frame dependent. There are no invariants corresponding to "gravitational time dilation" for objects that are falling into the black hole.

For a static clock, yes, you can meaningfully define a "time dilation" relative to distant observers. But you can't for an infalling clock.

O-S calculated the *proper* time along an infalling worldline. That's not the same as calculating a time dilation; they didn't do that for an infalling object, because it can't be done. There is no invariant relationship between the proper time O-S calculated for an infalling object and any sort of "time dilation".

harrylin

The 2007 paper gives a clear conclusion about pure GR in a separate GR discussion; however the 2009 paper doesn't as clearly separate GR from GR+QM, and so I did not spot or understand what error in the "classical" GR calculation was supposedly demonstrated in the 2009 paper - or even if they claim that they did.
Please clarify what the claimed error is according to you - I'm sure that you understand it much better than I do.

PAllen

Except that your interpretation of an alleged classical result is at odds with how every expert here reads the paper, how every expert here reads the press releases, and how other authors refer to the 2007 paper (it is considered new only insofar as the quantum result).
You are entitled to your interpretation, but it is important to note that it is considered incorrect by every expert here.

PAllen

SOL is a vernacular abbreviation I don't think I can render here. Google it. First urban dictionary meaning.

stevendaryl

In an early paper by Padmanabhan and Narlikar, the authors do challenge the classical notion of the Schwarzschild solution. The paper mentions black hole radiation, but most of the paper is really concentrating on classical black holes.

http://www.academia.edu/2120610/The_..._Physics_1988_

PAllen

Actually, I don't see any fundamental challenges to established understanding. The observation the information about the black hole is never in the past light cone of an external observer is standard. Stating that if new physics preventing actual horizons and BH in the real universe, physical theory would be 'in better shape' is also not a new idea or particularly controversial. In their conclusion, they also note that new physics is required to avoid the singularity as prediction of GR - there is no solution in classical GR. I also notice they don't address the singularity theorems at all, which is an unfortunate omission. They do mention negative energy as a way to avoid BH formation, which sidesteps the assumptions of the singularity theorems, but most would call that new physics - even within established quantum theory, inequalities governing negative energy imply it can't be a solution to the singularity problem of GR.

Despite the above caveats, it is also worth mentioning that this paper is very early in Padmanabhan's career (1987), and is published in a journal which at the time was a dumping ground for work unpublishable in mainstream journals.

harrylin

You are ducking my question. Please clarify what the claimed error is according to you.

PAllen

I don't believe the authors dispute the mainstream interpretation of BH formation except in light of the quantum result which allows a physical justification for saying part of the classical solution is not part of the universe - which goes beyond saying it is not observable by an external observer. Every expert here who has commented on the paper and press release interprets it this way, not as claiming any new classical interpretation.