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The gauge/gravity enables us to learn about quantum gravity by solving gauge theory. This is not an easy task, of course, and hence numerical techniques should play important roles. So far, properties of super Yang-Mills theories with Euclidean signature, such as the thermodynamic properties, have been studied by using Monte Carlo methods, and good agreement with the dual gravity prediction has been observed, including stringy corrections, both alpha prime and  and g_s. Still, the real-time properties are not well understood.

As a modest first step for the real-time study, we consider classical dynamics of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, which is expected to describe a highly stringy black hole in type IIA superstring theory. It turns out that this classical model has rather rich structure -- qualitative features of the thermalization of a black hole, the fast scrambling proposed by Sekino and Susskind, and a symptom of the evaporation. By taking into account a part of the quantum effect, we give a classical matrix model which can mimic the formation and evaporation of a black hole. We also argue that a similar calculation could be done for classical Yang-Mills theories with nonzero spatial dimension, without suffering from the UV catastrophe.

This talk is based on collaborations with S. Aoki, N. Iizuka (hep-th) and with E. Berkowitz, G. Gur-Ari, J. Maltz, S. Shenker (in progress).