[DrRocket]

Gary Anthony Kent, on 14 September 2011 - 11:15 PM, said:

Hawking did not retract? - i.e. He did not present a contradictory hypothesis? Does he not now propose that the information that points to matter which has fallen into a black hole still exists as a contribution to the total entropy of the black hole which exists as a sort of "image" on the"surface" of its event horizon? This information is NOT available again via Hawking radiation?

What else did I get wrong?

Kip Thorne's might be called the sour grapes of a sore loser.

Your post is far too long and unintelligible to address line by line.

You pretty much got everthing wrong, including the above, including the inane remark about Kip Thorne.

You might want to take a closer look at Hawking's concession, which has some logical gaps, including the use of the Ads/CFT correspondence which itself is an unproved conjecture of Maldecena datting from about 1997.

In short, you have no idea what in the hell you are talking about.

[*puffy* japanisthebest]

G Anthony, on 8 September 2011 - 12:53 PM, said:

Stephen Hawking retracted his paradoxical view that information must be lost when matter falls into a black hole. In place of this idea, his revised mathematics (validated many times by numerous workers) shows that information persists but is confined to the surface or "event horizon" of the black hole. "Hawking radiation" may then be emitted by such a black hole and the information becomes available again. The singularity that is predicted by general relativity (GR) results from extrapolation of GR to the logical extreme. But, it is still logical. The logic cannot be tickered with without destroying the whole ediface. 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?

If matter is compressed to infinite density, the gravitational field associated with its very existence becomes infinite as well. By GR, this means that as mass falls into a black hole, time itself must slow down whereupon its pace declines toward zero. The only weird thing about black holes is this effect. But, the very same thing is seen when temperature is reduced to near absolute zero when a perfect crystal is studied in the laboratory. One can only extrapolate along a straight line leading toward "zero" degrees Kelvin. One can never reach zero in the lab. The connection to black holes is direct.

What this really means is that matter inside all black holes is still crashing down toward the "center of gravity" but it will never actually get there, not even after 14.72 bilion years. But, the center itself exists as the center of gravity as long as an event horizon can be defined. As such, it possesses a gravitational field that has a very unique profile of potential versus radius.

The event horizon surface of a black hole is associated with a certain entropy linked to its surface area. It is also linked to a certain temperature which assures that information is still present and that Hawking radiation may be emitted therefrom. Such radiation may take hundreds of billions of years to significantly affect the mass that is retained in the black hole, however. But, this is just a detail.

Search "Stephen Hawking entropy black hole". There is a class of thermodynamics called "black hole thermodynamics". Hawking and Beckenstein used quantum mechanics and statistical thermodynamics to define S_BH, the total entropy of a black hole.

So, the singular nature of a black hole is not just conjecture. It is fact, by general relativity. In order to dispute it, one must also dispute GR.

This has huge implications to the hypothesis of "Dark Matter" and hypothetical "Dark Energy". See the thread "MOND, Prelude to Critique of the Universe" and the thread "Critique of the Universe" under Astronomy and Cosmology.

...my friends at school are reading this and i just simplified it for them... when stuff falls in a black hole... it never reaches the bottom...eh... i didn't really do details..

[guenter]

*puffy* japanisthebest, on 6 February 2012 - 03:42 PM, said:

...my friends at school are reading this and i just simplified it for them... when stuff falls in a black hole... it never reaches the bottom...eh... i didn't really do details..

Be careful, using "Anthony" as a reference, see the comment of DrRocket!

The proper time for an object to fall from the event horizon of a black hole with 3 billion sun masses e.g. to its center (the singularity) is about 13 hours.

[MigL]

Well I guess its time to add my two cents...

When a relatively massive star reaches the end of its sustainable fusion process, it eventually undergoes gravitational collapse. The remaining material which cannot be ejected by a massive stellar explosion, is more or less in free fall towards the geometric centre of the former star, now a black hole. Einstein's equations have the peculiar consequence that the stellar material can continue to exist forever in a state of free fall without ever reaching the bottom. This can be nearly visualised with a Penrose diagram. The space/time in the region of the black hole is so strongly curved that space and time become interchanged. If you are an outside observer, you see the stellar collapse slow down and come to a stop because the direction of time inside the black hole is 'perpendicular' to the direction of time as seen externally, i.e.the only thing in your future once inside the black hole, is a direction ( the geometric centre ).The experiences and observations of the infalling and outside observers are vastly different ( to say the least ). This is due to the purely classical nature of GR.

Stephen Hawking came along and introduced a bit of QM and Thermodynamics into this classical picture of black holes, much the same as Max Planck did with his quantization of black body radiation in 1900.. Planck's equation E=hv was a long way from QM which took at least another 25-30 yrs and 50-60 for QED. Similarily Hawking has given us S=kA, where S=entropy, A=area and k is a constant, but like Planck's itt is only a modest beginning. Entropy is very similar to heat capacity and is measured in cal/deg while area is in cm^2. Hawking's constant k, then has a value of about 10^41 cal/deg/cm^2. This is a very large proportionality constant, and since entropy is a measure of randomization, this shows the degree to which any infalling material / energy / information is randomized.

So yes, I will agree black holes have a temperature and therefore radiate, and so, if small enough will evaporate and eventually finish with a gamma ray explosion, during our universe's lifetime. But no, I don't agree that information could possibly be conserved after that degree of randomization.

[guenter]

Migl, I recommend to careful distinguish Free-fall coordinates, whereby the time coordinate is proper time, from any other coordinates, otherwise there is confusion. The picture of the frozen star, you mentioned, refers to the far distant Schwarzschild observer.

[guenter]

Sorry, there is another misunderstanding:

MigL, on 10 February 2012 - 12:43 AM, said:

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]

guenter, on 10 February 2012 - 01:51 PM, said:

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]

IM Egdall, on 10 February 2012 - 07:04 PM, said:

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.

This post has been edited by guenter: 11 February 2012 - 03:05 PM

[guenter]

MigL, on 10 February 2012 - 09:22 PM, said:

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.

Quote

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]

guenter, on 11 February 2012 - 10:50 AM, said:

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?

This post has been edited by IM Egdall: 11 February 2012 - 04:28 PM

[guenter]

IM Egdall, on 11 February 2012 - 04:25 PM, said:

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]

Quote

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.

This post has been edited by MigL: 13 February 2012 - 07:59 PM

[Temporocitor]

Quote

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]

MigL, on 13 February 2012 - 07:51 PM, said:

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.

PaulWDent, on 14 February 2012 - 04:00 AM, said:

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.

Quote

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.