On the role of chaos in the ADS/CFT connection

The question of how infalling matter in a pure state forms a Schwarzschild black hole that appears to be at nonzero temperature is discussed in the co ntext of the AdS/CFT connection. It is argued that the phenomenon of self-t hermalization in nonlinear (chaotic) systems can be invoked to explain how the boundary theory, initially at zero temperature self thermalizes and acq uires a finite temperature. Yang-Mills theory is known to be chaotic (class ically) and the imaginary part of the gluon self-energy (damping rate of th e gluon plasma) is expected to give the Lyapunov exponent. We explain how t he imaginary part would arise in the corresponding supergravity calculation due to absorption at the horizon of the black hole.