Bulk shape of brane-world black holes

We propose a method to extend to the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow the exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parametrized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat pancake for astrophysical sources.