User Tools

Site Tools


advanced_notions:hawking_radiation

Link to this comparison view

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)