I understand that suitable compactified strings in AdS correspond to conformal field theories (w/o gravity) living on the boundary space. What I do not get is the exact relationship between non-perturbative gravitational phenomena in the bulk and the CFT. All what I have seen are perturbative strings living on a certain background w/o any back reaction on this background. So how do I get realistic non-perturbative gravitational processes using AdS/CFT? What is e.g. the framework to describe a gravitational collapse like black hole formation, neutron star merger, cosmological expansion (dS instead of AdS) Brill waves etc. using AdS/CFT? Is there a way to extract non-stationary spacetimes from AdS/CFT in the context of string theory?