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advanced_notions:hawking_radiation

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*see also Black Hole *

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

$$ T= \frac{\hbar c^3}{8 \pi G M k_B} ,$$

where $k_B$ is the Boltzmann constant, $c$ the speed of light, $G$ the gravitational constant, $\hbar$ the reduced Planck constant and $M$ the mass of the black hole.

The temperature of a black hole is tiny. Putting in the numbers yields

$$ T= 6.169 \cdot 10^{-8} \text{ K } \ \frac{M_\odot }{M}, $$ where $M_\odot$ is the mass of the sun. In words this means that black hole with a mass equal to the mass of our sun would have a temperature of only $10^{-8}$ K. If the black hole is heavier, the temperature gets even tinier.

- For a nice explicit discussion of the question "Where does Hawking radiation originate?", see Hawking radiation, the Stefan-Boltzmann law, and unitarization by Steven B. Giddings

The motto in this section is: *the higher the level of abstraction, the better*.

This formula for the Hawking radiation shows why black holes are so important and interesting. In this little formula everything comes together:

- Quantum mechanics, in the form of $\hbar$
- Gravity, in the form of $G$

It tells us that black holes are laboratories for quantum gravity.

advanced_notions/hawking_radiation.1523200462.txt.gz · Last modified: 2018/04/08 15:14 (external edit)

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