Gravity and Large Black Holes in Randall-Sundrum II Braneworlds

Abstract

We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ℓ. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20ℓ. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution.