Charged Randall-Sundrum black holes and N = 4 super Yang-Mills in AdS2 x S2

We obtain some exact results for black holes in the Randall-Sundrum model with a single brane. We consider an extreme black hole charged with respect to a Maxwell field on the brane. The near-horizon geometry is determined. The induced metric on the brane and the black hole entropy are compared with the predictions of 4d General Relativity. There is good agreement for large black holes, with calculable subleading corrections. As a separate application, the bulk solution provides a gravitational dual for (strongly coupled, large N) N = 4 SYM in AdS2 x S2 for arbitrary relative size of AdS2 and S2.