Charged black holes in a generalized scalar-tensor gravity model

We study 4-dimensional charged and static black holes in a generalized scalar-tensor gravity model, in which a shift symmetry for the scalar field exists. For vanishing scalar field the solution corresponds to the Reissner-Nordstrom (RN) solution, while solutions of the full scalar-gravity model have to be constructed numerically. We demonstrate that these black holes support Galilean scalar hair up to a maximal value of the scalar-tensor coupling that depends on the value of the charge and can be up to roughly twice as large as that for uncharged solutions. The Hawking temperature T-H of the hairy black holes at maximal scalar-tensor coupling decreases continuously with the increase of the charge and reaches T-H = 0 for the highest possible charge that these solutions can carry. However, in this limit, the scalar-tensor coupling needs to vanish. The limiting solution hence corresponds to the extremal RN solution, which does not support regular Galileanscalar hair due to its AdS(2) x S-2 near-horizon geometry. (C) 2017 The Author(s). Published by Elsevier B.V.