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 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 2018/05/04 09:53 jakobadmin ↷ Links adapted because of a move operation2018/04/08 17:14 ↷ Links adapted because of a move operation2018/04/02 10:31 jakobadmin [Why is it interesting?] 2018/04/02 10:31 jakobadmin [Concrete] 2018/04/02 10:29 jakobadmin 2018/04/02 10:28 jakobadmin created Next revision Previous revision 2018/05/04 09:53 jakobadmin ↷ Links adapted because of a move operation2018/04/08 17:14 ↷ Links adapted because of a move operation2018/04/02 10:31 jakobadmin [Why is it interesting?] 2018/04/02 10:31 jakobadmin [Concrete] 2018/04/02 10:29 jakobadmin 2018/04/02 10:28 jakobadmin created Line 1: Line 1: ====== Hawking Radiation ====== ====== Hawking Radiation ====== + //see also [[advanced_notions:​black_hole]] //  ​  ​ Line 8: Line 8: ​ ​  ​  ​ + + $$T= \frac{\hbar c^3}{8 \pi G M k_B} ,$$ + + 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: ​ -  ​  ​ +  ​ + + 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]]. ​ 