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--- advanced_notions:hawking_radiation [2018/04/02 10:29]
jakobadmin
+++ advanced_notions:hawking_radiation [2018/04/02 10:31]
jakobadmin [Why is it interesting?]
@@ Line 8: / Line 8: @@
 <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
@@ Line 17: / Line 30: @@
 </note>
 <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>