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advanced_notions:hawking_radiation [2018/04/02 10:29] jakobadmin |
advanced_notions:hawking_radiation [2018/04/02 10:31] jakobadmin [Concrete] |
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+ | $$ T= \frac{\hbar c^3}{8 \pi G M k_B} ,$$ | ||
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+ | 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. | ||
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+ | The temperature of a black hole is tiny. Putting in the numbers yields | ||
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+ | $$ T= 6.169 \cdot 10^{-8} \text{ K } \ \frac{M_\odot | ||
+ | }{M}, $$ | ||
+ | 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. | ||
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+ | ---- | ||
* 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 |