Extreme charged black holes in a braneworld with a cosmological constant

Application of the AdS/CFT correspondence to the Randall-Sundrum models may predict that there is no static solution for black holes with a radius larger than the bulk curvature scale. When the black hole has an extremal horizon, however, the correspondence suggests that the black hole can stay static. We focus on the effects of cosmological constant on the brane on such extremal brane-localized black holes. We observe that the positive cosmological constant restricts the black hole size on the brane as in ordinary four-dimensional general relativity. The maximum black hole size differs from that in four-dimensional general relativity case due to the nonlinear term in the effective Einstein equation. In the negative cosmological constant case, we obtain an implication on the Newton constant in the Karch-Randall model.