# Einstein-Maxwell-scalar black holes: classes of solutions, dyons and extremality

## TL;DR

This paper classifies Einstein-Maxwell-scalar black hole models based on their coupling functions, compares dilatonic and scalarised solutions, and shows that dyons can have smooth extremal limits, analyzed via the entropy function formalism.

## Contribution

It introduces a classification scheme for EMS models and analyzes the extremal limits of scalarised dyons, highlighting the necessity of both electric and magnetic charges.

## Key findings

- Scalarised black holes can have smooth extremal limits with dyons.
- Classification of EMS models based on coupling functions.
- Both electric and magnetic charges are essential for extremal solutions.

## Abstract

Spherical black hole (BH) solutions in Einstein-Maxwell-scalar (EMS) models wherein the scalar field is non-minimally coupled to the Maxwell invariant by some coupling function are discussed. We suggest a classification for these models into two classes, based on the properties of the coupling function, which, in particular, allow, or not, the Reissner-Nordstr\"om (RN) BH solution of electrovacuum to solve a given model. Then, a comparative analysis of two illustrative families of solutions, one belonging to each class is performed: $dilatonic$ versus $scalarised$ BHs. By including magnetic charge, that is considering dyons, we show that scalarised BHs can have a smooth extremal limit, unlike purely electric or magnetic solutions. In particular, we study this extremal limit using the entropy function formalism, which provides insight on why both charges are necessary for extremal solutions to exist.