Charged Black Holes with Scalar Hair

Understand

We consider a class of Einstein-Maxwell-Dilaton theories, in which the dilaton coupling to the Maxwell field is not the usual single exponential function, but one with a stationary point.

• The theories admit two charged black holes: one is the Reissner-Nordstr{\o}m (RN) black hole and the other has a varying dilaton.
• For a given charge, the new black hole in the extremal limit has the same AdS$_2\times$Sphere near-horizon geometry as the RN black hole, but it carries larger mass.
• We then introduce some scalar potentials and obtain exact charged AdS black holes.