# Gauss-Bonnet black holes with a massive scalar field

## TL;DR

This paper demonstrates the existence of Gauss-Bonnet black holes with a massive scalar field in extended scalar-tensor-Gauss-Bonnet gravity, analyzing how scalar field mass affects black hole properties and their deviations from Schwarzschild solutions.

## Contribution

It provides the first numerical evidence of Gauss-Bonnet black holes with a massive scalar field across different coupling functions, including scalarization cases, and systematically studies their characteristics.

## Key findings

- Scalar field mass suppresses the scalar field and makes black holes resemble Schwarzschild solutions.
- Massive scalar fields expand the domain of black hole solutions for linear and exponential couplings.
- Scalar field mass influences bifurcation points and deviations from GR near bifurcation.

## Abstract

In the present paper we consider the extended scalar-tensor-Gauss-Bonnet gravity with a massive scalar field. We prove numerically the existence of Gauss-Bonnet black holes for three different forms of the coupling function including the case of spontaneous scalarization. We have performed a systematic study of the black hole characteristics such as the area of the horizon, the entropy and the temperature for these coupling functions and compared them to the Schwarzschild solutions. The introduction of scalar field mass leads to a suppression of the scalar field and the increase of this mass brings the black holes closer to the Schwarzschild case. For linear and exponential coupling, a nonzero scalar field mass expands the domain of existence of black holes solutions. Larger deviations from the GR case are observed only for small masses and these differences decrease with the increase of the scalar field mass. In the case of a coupling function which leads to scalarization the scalar field mass has a significant influence on the bifurcation points where the scalarized black holes branch out of the Schwarzschild solution. The largest deviation from the case with a massless scalar field are observed for black hole masses close to the bifurcation point.