# The Naked Scientists Forum

### Author Topic: Do black holes violate the second law of thermodyn  (Read 7315 times)

#### realmswalker

• Sr. Member
• Posts: 205
##### Do black holes violate the second law of thermodyn
« on: 05/10/2006 02:06:58 »
Black holes suck in matter, and prevent it from being chaotic, eventually condensing it into a single point, what could be more ordered that that?
How does this conform witht he fact that entropy must always increase?
As black holes exist more and mroe (as they will when the universe advances) eventually all matter ought to be caught in them, and therefore entropy must not increase...

idk maybe im wrong...

#### another_someone

• Guest
##### Re: Do black holes violate the second law of thermodyn
« Reply #1 on: 05/10/2006 02:46:00 »
quote:
Originally posted by realmswalker
Black holes suck in matter, and prevent it from being chaotic, eventually condensing it into a single point, what could be more ordered that that?
How does this conform witht he fact that entropy must always increase?
As black holes exist more and mroe (as they will when the universe advances) eventually all matter ought to be caught in them, and therefore entropy must not increase...

idk maybe im wrong...

Aside from Hawkins radiation, which will recover some of that entropy, I would guess (but may myself be wrong) be two other issues.

Firstly, if you cannot look inside the event horizon, then you cannot know what is happening to entropy within there.

Secondly, does matter actually ever reach the centre of a black hole – I don't know.  Matter will be locked in to the black hole, and will approach the singularity, but will it actually ever reach it in less than an infinite timescale (ofcourse, the other question within a black hole, whose timescale, since different observers will see time differently)?

George

#### DocN

• Full Member
• Posts: 94
##### Re: Do black holes violate the second law of thermodyn
« Reply #2 on: 09/10/2006 17:15:38 »
S_{BH} = \frac{kA}{4l_{\mathrm{P}}^2}

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Do black holes violate the second law of thermodyn
« Reply #3 on: 09/10/2006 17:48:05 »
I'm sorry DocN, could please explain that formula?

About entropy and black holes, there have been many articles on Scientific American. If I found one I post the essence of it.

This subject has been debated in physics for decades; Hawking also made a bet with another scientist, Jacob Bekenstein; Hawking believed the information contained in a body vanishes after that body has entered into the black hole, the other scientist believed it was conserved.

Recently, Hawking changed idea, and he also claimed to have found a prove of it (but not all are totally convinced of this prove).

What I remember of this theory is that event horizon acts as a sort of "ultimate" microscope at the level of the strings; this because of the relativistic "stretching" of a body in a region of high gravitational fields.

Every single bit of information a body had before entering into the black hole is taken into the event horizon as a sort of an enlarged picture of it. The total area of the event horizon is proportional to the black hole's entropy and the total entropy of the universe + black hole, obeys the second principle of thermodinamics.

http://en.wikipedia.org/wiki/Black_hole_thermodynamics
« Last Edit: 09/10/2006 18:01:12 by lightarrow »

#### DocN

• Full Member
• Posts: 94
##### Re: Do black holes violate the second law of thermodyn
« Reply #4 on: 09/10/2006 21:52:32 »
Starting from some theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon. Later, Stephen Hawking showed that black holes emit thermal Hawking radiation corresponding to a certain temperature (Hawking temperature). Using some arguments rooted in thermodynamics, Hawking was also able to calculate the entropy that the black hole must carry. The result confirmed Bekenstein's conjecture:

S_{BH} = frac{kA}{4l_{mathrm{P}}^2}

where k is Boltzmann's constant, and l_{mathrm{P}}=sqrt{Ghbar / c^3} is the Planck length. The black hole entropy is proportional to its area A. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle. The subscript BH either stands for "black hole" or "Bekenstein-Hawking".

from--Wikipedia.
Doc

#### Zeig

• Jr. Member
• Posts: 12
##### Re: Do black holes violate the second law of thermodyn
« Reply #5 on: 13/10/2006 00:31:39 »
wow...thats a good question..hmm..i guess my answer not using much of a scientific suport would be, everything has to be in somthing. easy as that, no? well what i  mean is that you have a book well that book is in a box, the box is in the room, the room is in the building, the building is in the lower atmosphere, ect. so wouldn't eventualy if everything is within one black hole (if they eat eachother after they get everything els) wouldn't all the matter be back to one place again and just as a dencer form start of life again? to top that what is space in? how do we not know we are the denser forms of matter that once was a universe larger that our own?
« Last Edit: 13/10/2006 00:31:52 by Zeig »

#### another_someone

• Guest
##### Re: Do black holes violate the second law of thermodyn
« Reply #6 on: 13/10/2006 17:56:05 »
quote:
Originally posted by DocN
Starting from some theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon.

The black hole entropy is proportional to its area A. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle.

I am afraid my small brain is unable quite to get around this.

If the maximal entropy is proportionate to area, then how can it be the maximal for the volume?  Volume and area are not the same thing?

George

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Do black holes violate the second law of thermodyn
« Reply #7 on: 14/10/2006 11:10:49 »
quote:
Originally posted by another_someone

If the maximal entropy is proportionate to area, then how can it be the maximal for the volume?  Volume and area are not the same thing?
http://en.wikipedia.org/wiki/Holographic_principle

quote:
"...so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume."

So, it's not possible to fix volume and area of that region independently one of the other: if I consider a region of space  with a given volume, I cannot arbitrarily increase its area to infinite, for example warping it into a table-like shape, because the largest black hole which can fit inside it couldn't be larger than the table tickness. At least, this is how I have understood it.
« Last Edit: 14/10/2006 11:18:40 by lightarrow »

#### another_someone

• Guest
##### Re: Do black holes violate the second law of thermodyn
« Reply #8 on: 14/10/2006 17:33:05 »
quote:
Originally posted by lightarrow
http://en.wikipedia.org/wiki/Holographic_principle
quote:
"...so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume."

So, it's not possible to fix volume and area of that region independently one of the other: if I consider a region of space  with a given volume, I cannot arbitrarily increase its area to infinite, for example warping it into a table-like shape, because the largest black hole which can fit inside it couldn't be larger than the table tickness. At least, this is how I have understood it.

Sorry, I still don't understand.

I was not suggesting that the shape would be anything but spherical, but nonetheless, the surface area is proportional to the square of its radius, while the volume proportional to the cube of its volume.  This implies that the larger the black hole, the smaller the volume density of entropy, because the entropy is merely increasing quadratically, while the volume continues to expand cubically.  In other words, the sum of the entropy of lots of small black holes filling a volume would be less than the entropy of a single black hole filling that same volume, so how can a single black filling a given volume be considered of maximal entropy.

I suppose one problem is that I probably do not properly understand how one should sum two or more entropy spaces.

George

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Do black holes violate the second law of thermodyn
« Reply #9 on: 14/10/2006 18:20:59 »
quote:
Originally posted by another_someone

Sorry, I still don't understand.

I was not suggesting that the shape would be anything but spherical, but nonetheless, the surface area is proportional to the square of its radius, while the volume proportional to the cube of its volume.  This implies that the larger the black hole, the smaller the volume density of entropy, because the entropy is merely increasing quadratically, while the volume continues to expand cubically.  In other words, the sum of the entropy of lots of small black holes filling a volume would be less than the entropy of a single black hole filling that same volume, so how can a single black filling a given volume be considered of maximal entropy.
This weirdness happens with black holes only, not with ordinary matter; it's the essence of the "holographic principle": two dimensions seems to be enough to describe every information in the universe, as if we were nothing else than a "3-D holography" of a 2-D surface.

quote:

"This is counter-intuitive to physicists because entropy is an extensive variable, being directly proportional to mass, which is proportional to volume (all else being equal, including the density of the mass).

If entropy of ordinary mass (not just black holes) is also proportional to area, then this implies that volume itself is somehow illusory: that mass occupies area, not volume, and so the universe is really a hologram which is isomorphic to the information "inscribed" on its boundaries [3]."

When I read it for the first time, I was upset too.
« Last Edit: 14/10/2006 18:30:20 by lightarrow »

#### another_someone

• Guest
##### Re: Do black holes violate the second law of thermodyn
« Reply #10 on: 14/10/2006 20:23:40 »
quote:
Originally posted by lightarrow
If entropy of ordinary mass (not just black holes) is also proportional to area, then this implies that volume itself is somehow illusory: that mass occupies area, not volume, and so the universe is really a hologram which is isomorphic to the information "inscribed" on its boundaries [3]."

When I read it for the first time, I was upset too.

This would be a fascinating, but peculiar, concept.  Not least, it should imply that with the continued expansion of the universe, we should see a continued reduction in entropy density; yet the second law of thermodynamics implies that entropy should increase, not reduce.

It is true that the second law only applies to an entire closed system, and does not disallow a reduction of local entropy so long as the total universal entropy increases; but  do we have any evidence that local entropy density is decreasing in this manner?

George
« Last Edit: 14/10/2006 22:59:24 by another_someone »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### Re: Do black holes violate the second law of thermodyn
« Reply #11 on: 15/10/2006 12:31:55 »
Why should entropy density be more important than entropy itself? The second law refers to entropy, not to entropy density.
« Last Edit: 15/10/2006 12:34:15 by lightarrow »

#### another_someone

• Guest
##### Re: Do black holes violate the second law of thermodyn
« Reply #12 on: 15/10/2006 14:24:25 »
quote:
Originally posted by lightarrow
Why should entropy density be more important than entropy itself? The second law refers to entropy, not to entropy density.

This is true, but the second law, like all physical laws that we understand, relates to our own experience of the universe, and not the universe in its totality.  Our own experience of the universe is within what is essentially a fixed volume, and thus our validation of the second law of thermodynamics is within that fixed volume (which is, if we are correct about an expanding universe, an ever smaller percentage of the total universe).

In the whole scheme of things, across the entire universe, you are right that it is the totality of the entropy that is more important than the density; but within our experience of the universe, it is the entropy within a fixed volume that is important, which would correlate to the entropy density.

I accept that what we are talking about is nonetheless about local entropy density, and not universal average entropy density; but nonetheless, if local entropy density is seen to increase, while theory were to tell us that universal entropy density should reduce, we would have to find some way of explaining that discrepancy.

George
« Last Edit: 15/10/2006 14:28:25 by another_someone »

#### The Naked Scientists Forum

##### Re: Do black holes violate the second law of thermodyn
« Reply #12 on: 15/10/2006 14:24:25 »