In this talk I first review a new method, borrowed from the Ricci Flow literature, to solve (numerically) the Einstein equations for static spacetimes. The method is based on a generalisation of the usual harmonic-coordinate gauge fixing and, as I will show, it is governed by a maximum principle which allows one to rule out the existence of Ricci solitons in favourable circumstances. As a first application of the method I will show how to construct (using Ricci Flow) the gravitational dual of N=4 super Yang-Mills on the background of the 4d Schwarzschild black hole. This provides the first quantitative calculation of a stress tensor of a strongly coupled 4d field theory in the background of a black hole. As a second application, I will construct localised black holes on a 3-brane in the context of Randall-Sundrum infinite braneworld scenario. Our work provides evidence for the existence of braneworld black holes of any size, therefore disproving some old conjectures in the literature.