The Black Hole War Part 2

Part 3 please.

Hi Matthew,

Welcome to CR4. Since there doesn't seem to be much interest, there wont be a part 3, but I will share the theories here one at a time.

Item 5. According to Susskind, a thermometer lowered to the vicinity of a black hole will report a very high temperature at the stretched horizon (1 Planck length thick above the horizon). To a free-falling observer it is normal empty space and a non event. [I don't buy it] To go with that (I guess) Susskind proposed black hole complementarity. Information is both reflected at the event horizon and passes through the event horizon and can't escape, with the catch being that no observer can confirm both stories simultaneously.

Regards.

-S

I think that BHs must be the most long-living macroscopic objects in the universe (especially the huge ones, like those located in the center of many galaxies). Consider a huge BH. As it slowly devours the matter and energy from the nearby space (e.g. attracting the mass of a companion star, creating an accretion disc around its event horizon and, finnaly, absorbing all that mass), its mass (and its event horizon) is increased gradually. As a result, the BH's temperature -already extremely low- is reduced further more, approaching the absolute zero. In the far future, there will be nothing left for the BH to "eat". It will be standing there alone, and, beyond that, Hawking's radiation will start to increase BH's temperature gradually. Its mass and size will start to decrease (due to this radiation), although extremely slowly. As its size is reduced this radiation becomes more and more significant. Finally, its life will end up with an energy explotion: BH will be evaporated and disappeared. And all this procedure will take a vast time duration.

...Hawking's radiation will start to increase BH's temperature gradually. Its mass and size will start to decrease (due to this radiation), although extremely slowly. As its size is reduced this radiation becomes more and more significant. Finally, its life will end up with an energy explosion: BH will be evaporated and disappear

You are right. Susskind says that no black hole is currently evaporating - they are all absorbing energy and growing. In a few hundred billion years they will evaporate very slowly (from Hawking radiation). It will take at least 10⁶⁰ years to detect any change.

Hello Standards Guy,

Sorry about the lack of interest from others. Perhaps the content is rather too hard for others to grasp. Now, what about time travel through a black hole? Possible or not? Through the horizon, to the past or the future?

Now, what about time travel through a black hole? Possible or not? Through the horizon, to the past or the future?

Susskind says "Black holes are not gateways to heaven, hell, other universes, or other places in our universe (Einstein-Rosen bridges do not happen)."

I don't see you commenting on the items above either. What is your take on item 3 above?

Item 1: Do I understand the question correctly? Are you confused about the ratio of information versus radius?

If so, the amount of information contained in a black hole is equivalent to the surface area of the event horizon.

Item 2: There is nothing in the equations that prevent time from running in reverse, but no one has found the reverse switch as of yet. Guess we will have to read the manual after all.

From the perspective of the math, nothing prevents it. I guess it will have to remain a theory for the time being.

Item 3: You mischaracterized the problem. It is not the difference in percent from some arbitrary temperature (i.e., 346K), but the percentage change from the initial state of 1E-8 to 1E-17. Does that make sense?

Item 4: Who knows?

Item 1...Are you confused about the ratio of information versus radius?

No, Susskind made that clear. On the idea (apparently it's just a theory) that the Planck length is the smallest possible size (the dimensions of the universe are quantized), I was questioning can anything change less than the Planck length (would changes also be quantized). If so, the radius of the BH in this example could not change by such a small amount, and therefore would remain the same size. Am I making myself clear?

Item 2...There is nothing in the equations that prevent time from running in reverse

I think you've hit the nail on the head. It's all mathematical. The math doesn't care if time goes backward, but AFAIK, it never has.

Item 3: You mischaracterized the problem. It is not the difference in percent from some arbitrary temperature (i.e., 346K), but the percentage change from the initial state of 1E-8 to 1E-17.

One temperature (1E-17) is technically a billion times colder than the other. But this book was written for general readers. From our point of view (346K), the two temps are almost exactly the same (within a billionth of a percent). So I find Susskinds statement to be highly misleading, and even irresponsible. You don't agree?

Item 4 was food for thought. I know there are several theories for inflation as part of the BBT. This kind of "jumped out at me" when I discovered the temperatures were the same.

Item 1: No, I am not sure I follow.

Item 1: i feel the issue is quantization of action. Can a change smaller than the plank's length be possible. Well, on such a microscopic scale I feel that smaller changes are not possible. The value 10^-72 meters (much smaller than the Planck length) might not result in a physical change in dimension.

So, if I understand the problem, it is more like this:

If you increase the circumference of a circle by one plank unit, what is the change of the radius?

Is that the crux of the argument?

Not quite. Does the BH horizon remain the same until enough matter is added to increase the radius by 1 Planck unit? (Think of the stair-step change vs a continuous slope)

Well, the smallest component of matter is of what size?

Barring the unknown, everything we know of today in the way of matter is much larger than a plank unit (a proton is 1E20 times the size of a plank unit).

We can add quarks to the argument, but there is no way to know their actual size and they are considered theoretical point particles in the world of physics (unless you are discussing string theory).

Well, the smallest component of matter is of what size?

That is a very good question. Susskind talks about "adding one bit of information" (matter) to a BH. I think he didn't define it well. He seems to like string theory. I don't. So there may not be a particle that has a mass that small. That would eliminate the whole issue. This is one of several reasons why Hawking shouldn't have conceded.

Item 6.

The maximum amount of information that can be stuffed into a region of space is equal to the area of the region (not the volume). Adding one bit of information to a black hole of any size will increase the area of the horizon by one square Planck unit (Planck unit of area). The entropy of a black hole, measured in bits, is proportional to the area of the horizon, measured in Planck units (information = area). The maximum amount of information that can possibly be contained in any region of space can be stored in the boundary of the region using no more than one quarter bit per Planck area. Susskind thinks it should be redefined so it's one for one. All this lead up to his holographic principle: The universe filled with galaxies, stars, planets & people is a hologram, an image of reality coded on a distant two-dimensional surface.

The problem, as I see it, is where the boundary is (the two-dimensional surface). His explanation made no sense to me. The universe (as explained by Hawking and others) has no boundary.

I think you mean surface area, not area. I.e., surface area of the event horizon.

What was his explanation for the "boundary"?

The univers has no boundary because there is nothing outside our universe (unless you are thinking of Brian Green's theory of multiple universes contained within some infinite bulk).

If you travel outward you eventually end up back where you started, even if traveling in a straight line.

What was his explanation for the "boundary"?

I made no note about it, but if I remember correctly, it was that wherever you are, the boundary is farther out! Is that a far out theory, or what?

Item 7. How Stephen lost the war.

Here is my summary of Susskinds words [mine are in square brackets]:

• Black holes are enormously large, tangled "monster strings."
• Entropy is proportional to mass in a tangled string. For black holes, Entropy ~ Mass². In string theory, all things are made of one dimensional strings. When strings cross, they can sometimes rearrange. A loop may be able to stick out from the horizon and brake off. That would be a particle that could be emitted by Hawking radiation.
• Anti-de Sitter space (ADS) has negative curvature. In two dimensions, it is drawn as a circle. Things are distorted, like on our world maps, but reverse (things get smaller toward the edges of the circle). The space-time curvature in ADS creates a gravitational field that pulls objects to the center, even if there is nothing there. [I object - the force of gravity curves space, not the other way around.]
• Juan Maldacena found that space with 2 dimensions + time that includes QCD but not gravity is mathematically the same as 3 dimensions + time in anti de Sitter space with gravity. Ed Witten wrote a paper Anti De Sitter Space and Holography. He wrote "A black hole in the soup [de Sitter universe] is equivalent to an ordinary hot fluid of elementary particles …gluons." The war was over.
• Maldacena's discovery was a convoluted path that wandered through extremal black holes, Polchinski's D-branes, and Matrix theory. It confirmed the holographic principle. Stephen Hawking conceded in 2007 at age 65.

According to Susskind, the center of our galaxy contains a black hole with a Schwarzschild radius of ≈ a hundred million miles. Tell me how a piece of a string could stick out a hundred million miles past the singularity. He never hinted that this theory replaced the singularity.
Do you think Hawking should have conceded?