Hawking radiation / String Hagedorn temperature?

In summary, the conversation discusses the similarities between the Hagedorn temperature for strings and the equivalent temperature for Hawking radiation from a Planck mass black hole. It is noted that both temperatures are of the order of the Planck energy and that calculations can result in a difference of two orders of magnitude. It is suggested that this may provide a quantum explanation for how black holes are formed. The conversation also touches on various theories and models that could be used to calculate these temperatures, such as D9 Brane/Antibrane, Axion dilaton field, and AdS Atick-Witten theory.
  • #1
TeethWhitener
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I was playing around with numbers and found that the equivalent temperature for Hawking radiation from a Planck mass black hole is ~5×1030 K. Later, I saw that the Hagedorn temperature for strings (where the partition function is expected to diverge) is reported to be around ~1030 K. I thought "wow this is a really intriguing coincidence!" and then I started to wonder whether it's actually a coincidence. It could be that the string Hagedorn temperature demarcates a phase transition from "ordinary" matter to stringy black hole matter at sufficient energy density. If so, that (in my opinion) would mark a plausible and fairly impressive quantum-ish explanation of how black holes are formed.

Since I don't really know how the Hagedorn temperature was calculated, my question is this: Is it a coincidence? Or does this aspect of string theory actually predict a phase transition at the same order of magnitude that you would expect quantum effects to dominate a gravitational system (Hawking radiation from a Planck mass black hole)? Or is it a sleight of hand: maybe string theorists used what they know about Hawking radiation to come up with a plausible value for the Hagedorn temperature (which might give an estimate for some other parameter--such as string tension--that they'd like to know)?

A note: I have an advanced degree (in chemical physics), but I know nothing about string theory other than the pop-sci stuff, which is why I marked the thread "Basic." Be gentle :)
 
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  • #2
A very good question. I don't know it too. Never calculated anything like this with numbers. And the question would be how? And with what kind of model?
D9 Brane/Antibrane? Axion dilaton field with axion hair? AdS Atick-Witten theory? Instanton D field? ...
I think there will be a difference between Superstringtheory and M theory. But which and why, I don't know too.
Would be really interesting to get to know this. But we have some String Cracks here, who might help
 
  • #3
That's not coincidence. They are both of the order of Planck energy (divided by Boltzmann constant).

Since you are a chemical physicist, it may be illuminating for you to know that Planck distance (namely, inverse Planck energy times ##\hbar c##) is for gravity and string theory what Bohr radius is for chemistry and atomic theory.
 
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  • #4
Demystifier said:
That's not coincidence. They are both of the order of Planck energy (divided by Boltzmann constant).
At least from what I've seen, they're both 2 orders of magnitude less than the Planck energy. To me, this isn't really "of the order of Planck energy." That's why I'm wondering how the string Hagedorn temperature was estimated.
 
  • #5
TeethWhitener said:
At least from what I've seen, they're both 2 orders of magnitude less than the Planck energy.
When one performs actual calculations, one gets additional factors such as
$$\frac{E_{Planck}}{(4\pi)^2}$$
In this way one easily gets a result which is two orders magnitude smaller, despite the fact that the relevant energy is still the Planck energy ##E_{Planck}##.
 
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  • #6
So basically, since the Hagedorn temperature is related to the self-dual radius, and since we choose the self-dual radius to be on the order of the Planck length, the Hagedorn temperature will be on the order of the Planck temperature? Is that somewhat right?
 
  • #7
TeethWhitener said:
So basically, since the Hagedorn temperature is related to the self-dual radius, and since we choose the self-dual radius to be on the order of the Planck length, the Hagedorn temperature will be on the order of the Planck temperature? Is that somewhat right?
Yes.
 
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  • #8
Demystifier said:
Yes.
Excellent, thanks for your help!
 

Related to Hawking radiation / String Hagedorn temperature?

1. What is Hawking radiation?

Hawking radiation is a theoretical phenomenon proposed by physicist Stephen Hawking. It suggests that black holes emit radiation due to the quantum effects near the event horizon, causing them to slowly lose mass over time.

2. How does Hawking radiation relate to black holes?

Hawking radiation is directly related to black holes because it is thought to be emitted by them. As black holes absorb matter and energy, they also emit Hawking radiation, causing them to eventually evaporate.

3. What is the String Hagedorn temperature?

The String Hagedorn temperature is a theoretical limit in string theory that represents the maximum temperature in the universe. It is thought to be the temperature at which the strings that make up particles can no longer vibrate, leading to a breakdown of the laws of physics as we know them.

4. How does the String Hagedorn temperature affect Hawking radiation?

The String Hagedorn temperature plays a role in Hawking radiation because it sets the upper limit for the temperature at which black holes can emit radiation. As the black hole's temperature approaches the String Hagedorn temperature, the rate of Hawking radiation increases until the black hole eventually evaporates completely.

5. Is Hawking radiation and the String Hagedorn temperature proven to exist?

Hawking radiation and the String Hagedorn temperature are both theoretical concepts that have yet to be directly observed. However, they are based on well-established theories and have been supported by indirect evidence and mathematical calculations.

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