Instability of Schwarzschild Black Holes in Einstein-scalar-Gauss-Bonnet Gravity: Perturbative Approach and Time-Domain Analysis

TL;DR

This paper investigates the stability of Schwarzschild black holes in Einstein-scalar-Gauss-Bonnet gravity using perturbative and time-domain methods, revealing the emergence of stable scalarized solutions under certain couplings.

Contribution

It introduces a perturbative approach to analyze black hole instability and scalarization in Einstein-scalar-Gauss-Bonnet gravity, including nonlinear effects for the first time.

Findings

No stable scalarized solutions with quadratic coupling.

Stable scalarized solutions appear with quartic and exponential couplings.

Discrepancies suggest perturbative limitations in capturing full dynamics.

Abstract

We study the instability of Schwarzschild black holes and the appearance of scalarized solutions in Einstein-scalar-Gauss-Bonnet gravity performing a time-domain analysis in a perturbative scheme. First we consider a quadratic coupling function and we perform an expansion for a small perturbation of the scalar field around the Schwarzschild solution up to the second order; we do not observe any stable scalarized configuration, in agreement with previous studies. We then consider the cases of quartic and exponential coupling, using an expansion for small values of the Newton's constant, in order to include the nonlinear terms introduced by the coupling in the field equations; in this case we observe the appearance of stable scalarized solutions different from those found in literature. The discrepancy can be an artifact of the perturbative approach.