Small black holes on branes: Is the horizon regular or singular?

We investigate the following question: Consider a small mass, with ϵ (the ratio of the Schwarzschild radius and the bulk curvature length) much smaller than 1, that is confined to the TeV brane in the Randall-Sundrum I scenario. Does it form a black hole with a regular horizon, or a naked singularity? The metric is expanded in ϵ and the asymptotic form of the metric is given by the weak field approximation (linear in the mass). In first order of ϵ we show that the iteration of the weak field solution, which includes only integer powers of the mass, leads to a solution that has a singular horizon. We find a solution with a regular horizon but its asymptotic expansion in the mass also contains half integer powers.