# Static Gauss-Bonnet Black Holes at Large $D$

## TL;DR

This paper investigates the stability and perturbations of static Gauss-Bonnet black holes in large dimensions, revealing conditions for instability and the existence of new non-spherical solutions influenced by the Gauss-Bonnet term, charge, and cosmological constant.

## Contribution

It provides analytic expressions for quasinormal modes and constructs explicit non-spherical static solutions in large D Gauss-Bonnet gravity with a cosmological constant.

## Key findings

- Positive Gauss-Bonnet term leads to instability only with positive cosmological constant.
- Negative Gauss-Bonnet term causes black hole instability regardless of cosmological constant.
- Existence of static zero-mode perturbations indicates new non-spherical black hole solutions.

## Abstract

We study the static black holes in the large $D$ dimensions in the Gauss-Bonnet gravity with a cosmological constant, coupled to the Maxewell theory. After integrating the equation of motion with respect to the radial direction, we obtain the effective equations at large $D$ to describe the nonlinear dynamical deformations of the black holes. From the perturbation analysis on the effective equations, we get the analytic expressions of the frequencies for the quasinormal modes of charge and scalar-type perturbations. We show that for a positive Gauss-Bonnet term, the black hole could become unstable only if the cosmological constant is positive, otherwise the black hole is always stable. However, for a negative Gauss-Bonnet term, we find that the black hole could always be unstable. The instability of the black hole depends not only on the cosmological constant and the charge, but also significantly on the Gauss-Bonnet term. Moreover, at the onset of instability there is a non-trivial static zero-mode perturbation, which suggests the existence of a new non-spherically symmetric solution branch. We construct the non-spherical symmetric static solutions of the large $D$ effective equations explicitly.