Hawking radiation as tunneling from squashed Kaluza-Klein black hole

We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple manner, which was recently suggested by Umetsu, is possible to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. By using same manner, we derive both the desired result of the Hawking temperature and the effect of the back reaction associated with the radiation in the squashed Kaluza-Klein black hole background.

Clear evasion of the uncertainty relation with very small probability

We entertain the idea that the uncertainty relation is not a principle, but rather it is a consequence of quantum mechanics. The uncertainty relation is then a probabilistic statement and can be clearly evaded in processes which occur with a very small probability in a tiny sector of the phase space. This clear evasion is typically realized when one utilizes indirect measurements, and some examples of the clear evasion appear in the system with entanglement though the entanglement by itself is not essential for the evasion. The standard Kennards relation and its interpretation remain intact in our analysis. As an explicit example, we show that the clear evasion of the uncertainty relation for coordinate and momentum in the diffraction process discussed by Ballentine is realized in a tiny sector of the phase space with a very small probability. We also examine the uncertainty relation for a two-spin system with the EPR entanglement and show that no clear evasion takes place in this system with the finite discrete degrees of freedom.