Stephen Hawking retracted his paradoxical view

[guenter]

Sorry, there is another misunderstanding:

 

The space/time in the region of the black hole is so strongly curved that space and time become interchanged.

One can find this wording in some popular literature, but it is not correct to say so. The wristwatch of the freefaller shows still the flow of the time after he has crossed the event horizon. What happens in Schwarzschild coordinates is that the curvature factor is < 0 for r < 2M, which makes the t-coordinate spacelike and vice versa the r-coordinate timelike. So, these radial coordinates do interchange, not space and time.

[IM Egdall]

One can find this wording in some popular literature, but it is not correct to say so. The wristwatch of the freefaller shows still the flow of the time after he has crossed the event horizon. What happens in Schwarzschild coordinates is that the curvature factor is < 0 for r < 2M, which makes the t-coordinate spacelike and vice versa the r-coordinate timelike. So, these radial coordinates do interchange, not space and time.

 

Can you elaborate or give us a link on this please.

[imatfaal]

IME - my understanding is (and guenter will correct me if I am wrong) is that the interchange is due to the choice of coordinate systems - and thus it is an anomaly introduced by this mathematical choice rather than physical reality.

 

When dealing with blackholes, their event horizons, and interiors the choice of coordinate systems is crucial. The metric, if expressed in schwartzchild coordinates will become singular (div by zero) at the event horizon - but by use of other modified coordinate systems such as the eddington-finkelstein this problem is avoided. as we do not believe there is a massive discontinuity for a free-falling observer at the EH then it is best than the coordinate system allows the metric to be continuous.

[MigL]

Sorry guenter, maybe I oversimplified so that everyone can understand, and I wasn't specific enough for you.

However I believe both points you addressed were trivial and due to mis-understandings.

 

I believe I did state that the 'frozen star' concept applies to external observers only and that an infalling observer notices no abnormalities in the passing of time. And no I do not believe this to be caused by choice of co-ordinate system. It is an abnormality of space/time itself, and not of the mathematical model used to describe it.

And yes your time coordinate is spacelike since the infalling observer's future is a spatial direction ( to the centre of the black hole ) and no deviation is possible. But like I said, I used simple english.

 

But all that was secondary to the point I was trying to make, in response to G. Anthony that intact information could ever be re-radiated via Hawking radiation from a black hole. The black hole part was merely to 'introduce' the main point.

[guenter]

Can you elaborate or give us a link on this please.

 

Yes, here.

 

 

Frankly, I prefer the curvature factor in the form (1-2M/r), because it shows the influence of the Mass on the metric. The angle term is zero in case of a radial fall.

 

The point is that for r > 2M the sign of dt² is positiv and that of dr² negativ. Beyond the event horizon its just vice versa.

So, dt² and dr² change role at r = 2M. Its a consequence of the coordinate singularity at r = 2M.

 

It might be of interest that the mentioned coordinate singularity vanishes, if the Schwarzschild coordinates are transformed into Kruskal-Szekeres coordinates. Then the t- and r-coordinates remain timelike and spacelike.

Edited February 11, 2012 by guenter

[guenter]

But all that was secondary to the point I was trying to make, in response to G. Anthony that intact information could ever be re-radiated via Hawking radiation from a black hole. The black hole part was merely to 'introduce' the main point.

 

But no, I don't agree that information could possibly be conserved after that degree of randomization.

That sounds very natural, Migl. The Hawking radiation which is a black body radiation doesn't contain the missing information. But one should remember Leonard Susskind and his string theoretical calculations. According to that, the information is conserved at the horizon surface. I am not familiar with this stuff, but am sceptical. And - who knows whether string theory is more than a wonderful mathematical building.

[IM Egdall]

Yes, here.

 

 

Frankly, I prefer the curvature factor in the form (1-2M/r), because it shows the influence of the Mass on the metric. The angle term is zero in case of a radial fall.

 

The point is that for r > 2M the sign of dt² is positiv and that of dr² negativ. Beyond the event horizon its just vice versa.

So, dt² and dr² change role at r = 2M. Its a consequence of the coordinate singularity at r = 2M.

 

It might be of interest that the mentioned coordinate singularity vanishes, if the Schwarzschild coordinates are transformed into Kruskal-Szekeres coordinates. Then the t- and r-coordinates remain timelike and spacelike.

 

Got it. Thanks guenter.What are the physical implications?

Edited February 11, 2012 by IM Egdall

[guenter]

Got it. Thanks guenter.What are the physical implications?

IM Egdall, one way to answer this question, might come from considering the lightcones. Perhaps you are familiar with that. They are vertical in flat space, getting tipped close to the Black Hole, are tangent at the horizon and are tipped inwards inside it.

 

Now imagine events in spacetime on a surface of constant r. Outside the horizon 2 events on this surface are related timelike, because one event is within the lightcone of the other one. At the horizon 2 events are separated lightlike (lightcone is tangent there). Inside the horizon events with constant r are related spacelike as according to the lightcones being tipped inwards. so, I guess the switching of coordinates results in how 2 events in spacetime are related to each other.

 

A similar consideration should hold for surfaces of constant time.

 

But my knowledge regarding your question is very limited. Hopefully one of the experts can tell more or, in case correct me.

[Temporocitor]

The trouble with singularities is only that one cannot do anything more with them, mathematically. They are a dead end. One can still say that matter therein must be compressed to infinite density, though. But, what does this mean?

 

 

 

It means we have to examine the meaning of infinity and infinitesimality. Let's imagine that the entire universe was one megagargantualithic black hole. The hole itself would be finite in it's mass, but at the singularity it would represent infinity approaching zero. Everything outside the biggest baddest black hole would represent infinity manifest.

[MigL]

Sorry its taken so long to get back Guenter.

 

I realise that the source of Hawking radiation is virtual particles of the vacuum surrounding the event horizon, but they do affect the event horizon. For sufficiently small black holes such that their lifetimes coincide with the lifetime of the universe, ie. they can evaporate, the 'incorporated' virtual particles making up Hawking radiation shrink the surface area of the small black hole until the event horizon disappears and the 'contents spill back out in a gamma ray explosion.

So if the information is greatly randomized by entropy into the surface area of the event horizon like a giant book where all the pages are ripped out and tossed in the air ( example by Brian Green ), it is no longer available ( just like entropy 'renders' energy unuseable or unable to do work ) and, so I think, not preserved. It then disappears altogether when the black hole evaporates. So even if you want to say it is 'somehow preserved on the horizon's surface, according to Hawking's own ideas, eventually this surface disappears.

 

I know very little about string theory myself, other than the basics and am not familiar with Susskind's work. But Hawking's resoning for information conservation seems to be based on Quantum mechanical considerations. Maybe its too early to start mixing the apples and oranges of the classical and quantum. Sometimes it works as in Hawking's entropy/temperature/radiation picture, but maybe it doesn't hold up for information since one of his ideas implies the other is wrong.

Edited February 13, 2012 by MigL

[Temporocitor]

It then disappears altogether when the black hole evaporates. So even if you want to say it is 'somehow preserved on the horizon's surface, according to Hawking's own ideas, eventually this surface disappears.

 

 

 

What happens to the depleted energy or radiated particles? Although it may evaporate away from the EH, it certainly would be recaptured by the gravity and the internal inertia developing from within the light cone. The question that arises in such a case is does the gravity forming such an electromagnetic cone to begin with push the depleted energum into the cone or is it pulled from the internal mass attraction? The effect from the classical physics perspective would be the same.

[PaulWDent]

Lots of good questions about Black Holes to which I want to add these:

 

I think I am right in saying that, the larger the Black Hole (i.e. the greater the radius of the event horizon), the smaller the gravity gradient at the event horizon. So matter falling in does not necessarily get torn apart while still outside. Especially if it falls in in a straight line plumb dead center. So imagine that situation.

 

Now, just before the matter enters the Black Hole, it is not part of the Black Hole's mass, and the event Horizon radius is determined only by the mass inside. After it has fallen in, the Black Hole's mass and the radius of its event horizon must increase.

 

So, the $64000 question is: At what point does the Black Hole's event horizon radius increase? Does it come out to meet the falling in mass like a big snake's mouth opening up? If so, does the Black hole get a bulge on one side? And does that bulge subside as the matter plummets towards the central singularity? I have a big problem with the latter, because that implies we are getting information on the outside about what is happening inside.

 

I have other reasons to want to believe that mass can never be absorbed by a Black Hole except in a spherically symmetric manner. Or maybe in a cylindrically symmetric manner at least, if there is angular momentum involved, but I strongly prefer the spherically symmetric constraint, at least when there is no angular momentum involved. In the latter case, the matter thus covers the event horizon uniformly and continues its chute towards the central singularity as a sphere of collapsing radius.

 

Does anybody have any opinions or math on this?

[guenter]

So even if you want to say it is 'somehow preserved on the horizon's surface, according to Hawking's own ideas, eventually this surface disappears.

 

I know very little about string theory myself, other than the basics and am not familiar with Susskind's work.

So am I, Migl. Much simplified Susskind's point seems, that for a hypothetical observer at the EH, the information is somehow (keyword holographic principle) encoded in the EH. And as the EH shrinks the corresponding information is set free to the oustside. In other words, the encoded information decreases proportional to the loss of mass. So, the total information is conserved. The underlying mathematical concept (based on string theory) is very demanding but is taken serious by physicists.

 

I think I am right in saying that, the larger the Black Hole (i.e. the greater the radius of the event horizon), the smaller the gravity gradient at the event horizon. So matter falling in does not necessarily get torn apart while still outside.

I guess you talk about tidal forces. These are stretching things radially and squashing them perpendicular to that direction during their fall towards a mass. At the event horizon of a static black hole of mass M these forces are proportional to 1/M². So, if the BH is large enough, you may not even notice anything, while crossing the EH. Also, this dependence of the tidal forces on the BH's mass is the reason why the Hawking radiation increases with decreasing mass.

 

So, the $64000 question is: At what point does the Black Hole's event horizon radius increase? Does it come out to meet the falling in mass like a big snake's mouth opening up? If so, does the Black hole get a bulge on one side? And does that bulge subside as the matter plummets towards the central singularity? I have a big problem with the latter, because that implies we are getting information on the outside about what is happening inside.

According to theory black holes can be deformed by external fields. This happens dramatically during the merger of two black holes, creating gravitational waves thereby. If the infalling mass is small, this effect is tiny accordingly. Im am not sure but doubt that the dynamic is fully understood in such detail, as you are questioning. But for sure the Schwarzschild radius rs grows according to rs = 2M.

[JohnStu]

Good news for me I guess. His decisions is similar to my thoughts before.