April 9, 2009

Institute for the Physics and Mathematics of the Universe (IPMU)

Hirosi Ooguri and Masahito Yamazaki of the Institute for the Physics and Mathematics of the Universe developed a new method to use crystal melting models in three dimensions to identify quantum states of black holes in superstring theory.

The result of this study will appear in the science journal ** Physical Review Letters**.

Publication: *Physical Review Letters*

Title: Emergent Calabi-Yau geometry

Authors: Hirosi Ooguri, Masahito Yamazaki

### CONTACTS

## For more details- Hirosi Ooguri,
Professor e-mail. h.ooguri _at_ gmail.com |
## Media Contact- Fusae Miyazoe,
IPMU Press Officer e-mail. press _at_ ipmu.jp |

### SUMMARY

In 1974, Stephen Hawking showed that black holes, though they are completely dark as classical solutions to the Einstein equation, emit heat and evaporate by quantum effects.If this phenomenon obeys the laws of statistical mechanics, there must be an enormous amount of quantum information stored in a black hole (*1).

The IPMU researchers have shown that each quantum state of a particular class ofblack holes in string theory corresponds one-to-one to a molten crystal in threedimensions. For example, an ice is a crystal of water molecules. When it melts, it startslosing molecules from its corners. Similarly, the space-time without a black hole is aperfect crystal. As the crystal loses molecules, the black hole grows larger. In thethermodynamic limit, where the size of individual atoms becomes negligible, theyshowed that smooth space-time emerges and Hawking’s prediction is reproduced.

*1 According to Hawking’s computation, a black hole of M kg has exp(10^{16} M^{2}) quantum states. For example, a typical astrophysical black hole formed by stellar collapse weighs about 10^{31} kg and carries as many as e10^{78}states.

IPMU aims at understanding the origin, fate, and fundamental laws of the Universe, and was established by the World Premier International Research Center Initiative (WPI) program of Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. This research was supported in part by Global COE program of MEXT.