Spectral methods in general relativity and large Randall-Sundrum II black holes

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS sub(5)-CFT sub(4) solution to the Einstein equation with a negative cosmological constant [Lambda] that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS sub(5)-CFT sub(4) solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-[Lambda]M super(2)), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4-7/(-[Lambda]).