Gravity and large black holes in Randall-Sundrum II braneworlds

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.