advanced_notions:hawking_radiation

Next revision | Previous revision | ||

advanced_notions:hawking_radiation [2018/04/02 10:28] jakobadmin created |
advanced_notions:hawking_radiation [2018/05/04 09:53] (current) jakobadmin ↷ Links adapted because of a move operation |
||
---|---|---|---|

Line 1: | Line 1: | ||

====== Hawking Radiation ====== | ====== Hawking Radiation ====== | ||

+ | //see also [[advanced_notions:black_hole]] // | ||

<tabbox Intuitive> | <tabbox Intuitive> | ||

Line 8: | Line 8: | ||

| | ||

<tabbox Concrete> | <tabbox Concrete> | ||

+ | |||

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

+ | |||

+ | 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 [[https://arxiv.org/abs/1511.08221|Hawking radiation, the Stefan-Boltzmann law, and unitarization]] by Steven B. Giddings | * For a nice explicit discussion of the question "Where does Hawking radiation originate?", see [[https://arxiv.org/abs/1511.08221|Hawking radiation, the Stefan-Boltzmann law, and unitarization]] by Steven B. Giddings | ||

Line 17: | Line 30: | ||

</note> | </note> | ||

- | <tabbox Why is it interesting?> | + | <tabbox Why is it interesting?> |

+ | | ||

+ | 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 [[theories:speculative_theories:quantum_gravity|quantum gravity]]. | ||

</tabbox> | </tabbox> | ||

advanced_notions/hawking_radiation.1522657681.txt.gz · Last modified: 2018/04/02 08:28 (external edit)

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International