  We show how to construct low energy solutions to the Randall Sundrum II
(RSII) model using an associated AdS_5-CFT_4 problem. The RSII solution is
given in terms of a perturbation of the AdS-CFT solution, with the perturbation
parameter being the radius of curvature of the brane metric compared to the AdS
length \ell. The brane metric is then a specific perturbation of the AdS-CFT
boundary metric. For low curvatures the RSII solution reproduces 4d GR on the
brane. The leading correction is from local higher derivative curvature terms.
The subleading correction is derived from similar terms and also the dual CFT
stress tensor. Recently AdS-CFT solutions with 4d Schwarzschild boundary metric
were numerically constructed. We modify the boundary conditions to introduce
the RSII brane, and use elliptic numerical methods to solve the resulting
boundary value problem. We construct large RSII static black holes with radius
up to ~ 20 \ell. For large radius the RSII solutions are indeed close to the
associated AdS-CFT solution. In this case the local curvature corrections
vanish, and we confirm the leading correction is given by the AdS-CFT solution
stress tensor. We also follow the black holes to small radius << \ell, where as
expected they transition to a 5d behaviour. Our numerical solutions indicate
the RSII black holes are dynamically stable for axisymmetric perturbations for
all radii.
