# Black hole entropy problem

1. Apr 24, 2013

### Double-Slit

How can a black hole have a high entropy state if the matter inside it is in a supercondensed form with maximum density,which means less degrees of freedom therefore less entropy than normal matter.Like in neutron stars we have low entropy with the neutron degenerate matter and yet a black hole is just a step ahead from a neutron star and it has high entropy,how is that possible?

2. Apr 24, 2013

### jambaugh

In part it is a question of timing. If I said rather "the matter inside it will eventually be in a supercondensed form with maximum density..." would that sound better?

The "future" for an object crossing the BH's event horizon becomes detached from the future of external observers. From the external observer's viewpoint the infalling matter stops at the event horizon (and as it does this it causes the event horizon to expand beyond where it is). A realistic black hole is dynamic and fuzzy in that it has higher order moments. Its surface vibrates as it grows when an object "falls in" from one direction and it has charge moments as the infalling matter has a non uniform charge distribution. These will quickly propagate around the surface and get radiated away, the event horizon "rings" in a way emitting gravity waves and EM waves until it asymptotically settles down to the hairless charged spinning black hole. (Note this is Not Hawking's radiation but rather a classical effect.) But the interior configuration is from the outside observers extrapolated viewpoint a frozen tableau of infalling collapsing objects in space-time which cannot be observed and so are in one of a large number of configurations.

From the infalling observer's perspective you've fallen into a region of space that is quickly becoming small in a cylindrical way and hotter until you are stretched and pressed into an infinitely hot infinitely thin line. (Remember that inside the distance r from the "center" is a time axis. r is your Doomsday clock.

Last edited: Apr 24, 2013
3. Apr 24, 2013

### jambaugh

Some additional comments: I went into the Black hole "ringing" part because as an infalling object "detaches" from our universe it initially leaves a record in the BH's surface configuration of its own configuration as it enters. One could in principle extrapolate from the surface configuration just as the object is subsumed by the EH what its future behavior (along its time axis) will be aside from interacting with other infalling matter. But that info is quickly radiated away into space. That is part of the entropy increase. The BH after radiating this info away has a larger entropy than before.

4. Apr 24, 2013

### Double-Slit

By information radiated away,i think you mean the Hawking radiation which is radiation of light,which carry heat so that if radiated away with increase the heat,and therefore the entropy of the universe and decrease the entropy of the black hole.I guess thats vice versa as you said.

Yes i see,the classical effects of that electric discharge at the horizon may explain some,but i`m interested in the singularity,since it's described as an infinitessimally small point where the entire mass of the hole is located (Leaving aside the information imprint which is leaved at the horizon according to the Holographic principle).I still can't understand how can an infinitessimally small point have entropy,and if we consider the classical effects thats not really part of the hole,the real hole starts after you've crossed the horizon.Even if we consider the 2nd law of theormodynamics,can we interpret the black hole as a thermodynamically isolated system,with all this radiation it's emmitting?

5. Apr 25, 2013

### jambaugh

No, I was specifically not talking about Hawking rad. Take the extreme case of two merging BH's. As soon as their EH's intersect they become one larger non-spherical BH. The BH undergoes quadrapole oscillations radiating grav waves until it asymptotically settles down to a spherical configuration with surface area more than the sum of that of the two precursors. The increase in surface area and thus entropy exactly corresponds to this settling down and the radiation away of the non-zero multipole moments (which recorded the configuration of the earlier collision).

WRT the singularity, observe that it is a singularity in time. We derive Swarzschild's solution by solving Einstein's eqns under the constraints of static in time t, flatness at infinity, and spherical symmetry. We get a coordinate singularity at the event horizon. The reason is that our constraints can no longer be satisfied. We can remove the coordinate singularity by letting r (defined in terms of circumference) become time like. Interior to the static event horizon you get a non-stationary solution. It is that of a cylindrical collapsing universe.

I may have mispoke earlier about it getting hotter. I haven't checked if the tidal stretching in one direction matches the perp area contraction to yield net volume change. In short wether there is net compression.

 in addition, w.r.t. entropy at the zero hour the infallen matter is scattered along the singularity which is an infinitely long one dimensional null curve. Thus there is just enough room for entropy in the random order the matter gets shmeered along the singularity.

Last edited: Apr 25, 2013
6. Apr 28, 2013

### h_cat

What back holes? There is no such thing - at least from our point of view because no matter could ever be contracted beyond its schwarzschild radius. Even contracting to its schwarzschild radius would take infinite time. Nor can anything fall into a black hole because it would take infinite time to do so! Of course all from our system of reference.

vs_cat

7. Apr 28, 2013

### Staff: Mentor

The conclusion that there are no black holes and the claim that it would take an infinite time for a black hole collapse are both somewhere between misleading and just plain wrong.
(There are about 83 gigabazillion threads on this topic over in the relativity forum)

8. Apr 28, 2013

### h_cat

Nugatory, "just plain wrong" makes a fine argument. I don't know what formulas you use, maybe I got the wrong one but redshift goes to infinity at Rs in other words time stops at Rs.
(83 gigabazillion threads) if there are so many then it would be no effort for you to point me to a good one no?

t_0 = t_f \sqrt{1 - \frac{r_0}{r}}

va_cat

Last edited: Apr 28, 2013
9. Apr 29, 2013

### Staff: Mentor

Here are a a few, some better than others, but all at least moderately related to the physics at the event horizon and the relationship between the Schwarzchild time coordinate and the proper time of infalling and remote observers.
(probably best to continue this conversation over in the relativity forum; I see your thread there).

10. Apr 29, 2013

### h_cat

Thanks for the links, the spherical energy shell is a nice one but I didn't really found the same argumentation I did.

Seems I am not very welcome in the GR subforum. Some people mix science with religion. Theories are no dogmas and professors are no priests, Hawkins is not the Pope. But I may have got it all wrong and this is the catholic church's web-portal.

Anyway I think I put my arguments pretty clear. I do learn things by critic not by copying from a board.

mr_cat

11. Apr 29, 2013

### Bill_K

This paper by Bill Ames may help resolve your confusion. It describes what a collapsing star actually looks like to an outside observer as it passes through its Schwarzschild radius.

Last edited: Apr 29, 2013
12. Apr 29, 2013

### Mordred

Thanks for that link I prefer that to some of the other related links.

13. Apr 29, 2013

### Double-Slit

Who says anything about religion?Black holes do exist,it was confirmed definitely by NASA back in 2009 i guess or was it 2008.Anyhow of course we cant interact with matter infalling in it since:
the calculations described by you of the change of the electromagnetic spectrum due to immense gravity effects on the reflected light is pure mathematical concept.The definition of the singularity is by itself a 0 dimensional point.What is there nobody knows...Yet string theory assumes ridiculous extra dimensions beside the 4 that we can confirm and it still works.Can u imagine those,i dont think...Whether the mathematical validity of these reflect reality,thats philosophy ,but i guess we don't have a better tool.I personally think that those calculations are worthy and based on but not solely on that.Mathemathical logic,empiricism,rationality and a scientific method-al test should confirm those hypothesis if correct.

Anyhow this topic was about entropy change in a black hole where jambaugh made a really good point.Thanks,yet it's hard to comprehend,not to imagine an
around the singularity,even if it's mathematically correct.But i guess that just a flaw with the human species.

14. Apr 30, 2013

### Bill_K

It's much more interesting than that - the singularity is one-dimensional - it's being squeezed radially and stretched longitudinally. Jambaugh had it right:

15. Apr 30, 2013

### jambaugh

h_cat, if you read my exposition carefully you will see where I subtilly addressed the infinite time to fall in issue. In the limiting case of a effectively zero mass test particle infalling the external time to the fixed EH is indeed infinite. But for a massive particle in a finite time it will pass the EH for the larger BH formed by it plus the original.

It helps to view the stationary event horizon of a BH as the limiting case of the continuum of event horizons which form the future lightcones of events in our past. We can never escape these, and if there is enough mass in one region they can be bent inward to form a (3-)cylinder. Interior to this they are pointing inward pointing at the r=0 catestrophy.