# Instability mechanisms on asymptotically AdS black hole backgrounds

## TL;DR

This paper studies the stability of scalar fields on Reissner-Nordström-AdS black hole backgrounds, identifying mechanisms that cause the zero solution to become unstable under certain conditions.

## Contribution

It introduces two mechanisms explaining instability of the zero solution for the conformal scalar equation with defocusing nonlinearity on AdS black hole backgrounds.

## Key findings

- Identification of parameter regions where stability breaks down.
- Description of two distinct instability mechanisms.
- Insights into scalar field dynamics in AdS black hole spacetimes.

## Abstract

We investigate dynamics of the conformal scalar equation with defocusing cubic nonlinearity and Robin boundary conditions on the Reissner-Nordstr\"{o}m-anti-de Sitter background. At certain parts of the parameters phase space the zero solution ceases to be stable. We present two mechanisms responsible for this phenomenon.