# Einstein-scalar-Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows

## TL;DR

This paper develops an analytical approximation method for Einstein-scalar-Gauss-Bonnet black holes using continued-fraction expansion, enabling accurate calculations of black hole shadows and providing insights into their properties.

## Contribution

It introduces an analytical approximation technique for black hole solutions in Einstein-scalar-Gauss-Bonnet gravity, improving understanding and computational efficiency.

## Key findings

- Analytical expressions closely match numerical solutions.
- The method accurately predicts black hole shadows.
- Applicable to various coupling functionals.

## Abstract

Recently, numerical solutions to the field equations of Einstein-scalar-Gauss-Bonnet gravity that correspond to black-holes with non-trivial scalar hair have been reported. Here, we employ the method of the continued-fraction expansion in terms of a compact coordinate in order to obtain an analytical approximation for the aforementioned solutions. For a wide variety of coupling functionals to the Gauss-Bonnet term we were able to obtain analytical expressions for the metric functions and the scalar field. In addition we estimated the accuracy of these approximations by calculating the black-hole shadows for such black holes. Excellent agreement between the numerical solutions and analytical approximations has been found.