  Motivated by the gauge/gravity duality, we introduce a numerical scheme based
on generalized harmonic evolution to solve the Einstein field equations on
asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which
can be described by the (t,r,\chi,\theta,\phi) spherical coordinates adapted to
the R{\times}S3 boundary. We focus on solutions that preserve an SO(3) symmetry
that acts to rotate the 2-spheres parametrized by \theta,\phi. In the boundary
conformal field theory (CFT), the way in which this symmetry manifests itself
hinges on the way we choose to embed Minkowski space in R{\times}S3. We present
results from an ongoing study of prompt black hole formation via scalar field
collapse, and explore the subsequent quasi-normal ringdown. Beginning with
initial data characterized by highly distorted apparent horizon geometries, the
metrics quickly evolve, via quasi-normal ringdown, to equilibrium static black
hole solutions at late times. The lowest angular number quasi-normal modes are
consistent with the linear modes previously found in perturbative studies,
whereas the higher angular modes are a combination of linear modes and of
harmonics arising from non-linear mode-coupling. We extract the stress energy
tensor of the dual CFT on the boundary, and find that despite being highly
inhomogeneous initially, it nevertheless evolves from the outset in a manner
that is consistent with a thermalized N=4 SYM fluid. As a first step towards
closer contact with relativistic heavy ion collision physics, we map this
solution to a Minkowski piece of the R{\times}S3 boundary, and obtain a
corresponding fluid flow in Minkowski space.
