Rapid thermalization in field theory from gravitational collapse

Motivated by the duality with thermalization in field theory, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. We investigate the system numerically and establish that for small values of the initial amplitude of the scalar field there is no black hole formation, rather, the scalar field performs an oscillatory motion typical of geodesics in Anti de Sitter. For large enough values of the amplitude of the scalar field, we find black hole formation, which we detect numerically as the emergence of an apparent horizon. Using the time of formation as an estimate for thermalization in the field theory, we conclude that thermalization occurs very rapidly, close to the causal bound for a very wide range of black hole masses. We further study the thermalization time in more detail as a function of the amplitude and the width of the initial Gaussian scalar field profile and detect a rather mild structure.