# Unstable marginally outer trapped surfaces in static spherically symmetric spacetimes

## TL;DR

This paper investigates the stability and potential deformations of inner black hole and cosmological horizons in static spherically symmetric spacetimes, revealing that while infinitesimal deformations are possible, they do not extend to finite deformations.

## Contribution

It demonstrates that inner black hole and cosmological horizons can be infinitesimally deformed in certain spacetimes, but these deformations do not persist as finite changes, extending understanding of horizon stability.

## Key findings

- Inner horizons can be infinitesimally deformed
- Cosmological horizons can be translated in pure de Sitter
- Finite deformations of these horizons do not exist

## Abstract

We examine potential deformations of inner black hole and cosmological horizons in Reissner-Nordstr\"om de-Sitter spacetimes. While the rigidity of the outer black hole horizon is guaranteed by theorem, that theorem applies to neither the inner black hole nor past cosmological horizon. Further for pure deSitter spacetime it is clear that the cosmological horizon can be deformed (by translation). For specific parameter choices, it is shown that both inner black hole and cosmological horizons can be infinitesimally deformed. However these do not extend to finite deformations. The corresponding results for general spherically symmetric spacetimes are considered.