A long-standing puzzle in heavy ion physics is how the medium created in a collision thermalizes quickly enough to evolve hydrodynamically. An interesting place to start on this problem in the gauge-string duality is the time evolution of a black hole in anti-de Sitter space which starts off in a very anisotropic state, analogous to the highly compressed initial conditions of heavy ion collisions. A particular challenge is evolving an anti-de Sitter black hole through a highly non-linear oscillatory regime. An example of the results obtained (in terms of energy densities in the dual field theory) is shown below.
"Simulation of Asymptotically $AdS_5$ Spacetimes with a Generalized Harmonic Evolution Scheme" by H. Bantilan, F. Pretorius, and S. Gubser presents first results of a numerical scheme for solving Einstein's equations in asymptotically anti-de Sitter geometries. In particular, it shows that a particular set of initial conditions, corresponding to an anisotropically compressed fluid, can be evolved accurately to late times. The particular initial conditions studied have local equilibration built in, but this assumption is not necesssary for the evolution scheme.