Unstable marginally outer trapped surfaces in static spherically symmetric spacetimes

We examine potential deformations of inner black hole and cosmological horizons in Reissner-Nordström 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 the past cosmological horizon. Further, for pure de Sitter 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.