Electric charge on the brane?

We consider black holes localized on the brane in the Randall-Sundrum infinite braneworld model. These configurations are static and charged with respect to a spherically symmetric, electric Maxwell field living on the brane. We start by attempting to construct vacuum black holes, in which case our conclusions are in agreement with those of Yoshino in JHEP 0901:068, 2009 (arXiv:0812.0465). Although approximate solutions appear to exist for sufficiently small brane tension, these are likely only numerical artifacts. The qualitative features of the configurations in the presence of a brane U(1) electric field are similar to those in the vacuum case. In particular, we find a systematic unnatural behaviour of the metric functions in the asymptotic region in the vicinity of the AdS horizon. Our results are most naturally interpreted as evidence for the nonexistence of static, nonextremal charged black holes on the brane. In contrast, extremal black holes are more likely to exist on the brane. We determine their near-horizon form by employing both analytical and numerical methods. For any bulk dimension d>4, we find good agreement between the properties of large extremal black holes and the predictions of general relativity, with calculable subleading corrections.