# Analytical representation for metrics of scalarized Einstein-Maxwell black holes and their shadows

## TL;DR

This paper develops approximate analytical models for scalarized Einstein-Maxwell black holes, enabling accurate shadow calculations and revealing that scalarization enlarges black-hole shadows across various couplings.

## Contribution

It introduces a method to construct adjustable analytical representations of scalarized black hole metrics, validated by shadow calculations and provided with accessible Mathematica code.

## Key findings

- Scalarization increases black-hole shadow radius.
- Analytical forms achieve high accuracy with higher approximation order.
- The method is adaptable to different couplings and parameters.

## Abstract

Here we construct approximate analytical forms for the metric coefficients and fields representing the scalarized Einstein-Maxwell black holes with various couplings of the scalar field, once the parameters of the system are fixed. By increasing approximation order, one can obtain the analytic representation with any desired accuracy, what was tested via calculations of shadows for these black holes by using approximate analytical and accurate numerical metric functions. We share the Mathematica code which allows one to find an appropriate analytical form of the metric for any couplings and values of parameters. Scalarization increases the radius of the black-hole shadow for all the considered coupling functions.