Classical Gluon Radiation in Ultrarelativistic Nuclear Collisions: Space-Time Structure, Instabilities, and Thermalization

We investigate the space-time structure of the classical gluon field produced in an ultrarelativistic collision between color charges. The classical solution which was computed previously in a perturbative approach is shown to become unstable on account of the non-Abelian self-interaction neglected in the perturbative solution scheme. The time scale for growth of the instabilities is found to be of the order of the distance between the colliding color charges. We argue that these instabilities will eventually lead to thermalization of gluons produced in an ultrarelativistic collision between heavy nuclei. The rate of thermalization is estimated to be of order $g^2 \mu$, where $g$ is the strong coupling constant and $\mu^2$ the transverse color charge density of an ultrarelativistic nucleus.