Extremal black hole decay in de Sitter space

The decay of extremal charged black holes has been a useful guidance to derive consistency conditions in quantum gravity. In de Sitter space it has been argued that requiring (extremal) charged Nariai black holes to decay without forming a big crunch singularity yields the Festina Lente (FL) bound: particles with mass m_s and charge q should satisfy $m_s^2\gg M_p\mathit{Hq}$ \( {m}_s^2\gg {M}_p Hq \) , where M_p is the Planck mass and H the Hubble parameter. Using a tunneling approach we show that the decay probability of charged black holes in de Sitter space in the s-wave sector is P ∼ exp(∆S_b), where ∆S_b is the change in the black hole entropy. We find that the FL bound corresponds to ∆S_b ≤ – 1 in the Nariai and probe limit. However, taking into account backreaction we identify unsuppressed decay channels, which might be subdominant, that violate this bound but nonetheless do not result in a big crunch for every observer.