# Unstable horizons and singularity development in holography

## TL;DR

This paper investigates the development of singularities in holographic models where long-wavelength instabilities occur without a stable equilibrium phase, revealing that such instabilities can lead to arbitrarily large curvatures and finite-time singularities.

## Contribution

It identifies and analyzes a class of holographic scenarios lacking stable condensate phases, demonstrating the formation of finite-time singularities due to long-wavelength instabilities.

## Key findings

- Arbitrarily large curvatures develop near horizons during instability.
- Singularities form at finite boundary time without stable equilibrium.
- Certain holographic models exhibit no stable condensate phases.

## Abstract

In holographic applications one can encounter scenarios where a long-wavelength instability can arise. In such situations, it is often the case that the dynamical end point of the instability is a new equilibrium phase with a nonlinear scalar hair condensate outside the black hole horizon. We here review holographic setups where symmetric horizons suffer from long-wavelength instabilities where a suitable equilibrium condensate phase does not exist. We study the dynamics of the simplest model in this exotic class, and show that it uncovers arbitrarily large curvatures in the vicinity of the horizon which asymptotically turn such region singular, at finite time with respect to the boundary theory.