# Charged black holes in a generalized scalar-tensor gravity model

## TL;DR

This paper investigates charged black holes in a scalar-tensor gravity model, revealing how scalar hair and temperature vary with charge and coupling, and identifying the extremal Reissner-Nordström limit.

## Contribution

It introduces numerical solutions for charged black holes with scalar hair in a generalized scalar-tensor model, analyzing their properties and limits.

## Key findings

- Scalar hair exists up to a maximal coupling depending on charge.
- Hawking temperature decreases with charge, reaching zero at maximal charge.
- Extremal Reissner-Nordström solutions do not support scalar hair.

## Abstract

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-Nordstr\"om (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 $T_{\rm H}$ of the hairy black holes at maximal scalar-tensor coupling decreases continuously with the increase of the charge and reaches $T_{\rm H}=0$ 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 galilaen scalar hair due to its AdS$_2\times S^2$ near-horizon geometry.