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 $m_s^2\gg M_{p}Hq$, 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 $P\sim \exp (\mathrm{\Delta }{S}_b)$, where~$\mathrm{\Delta }{S}_b$ is the change in the black hole entropy. We find that the FL bound corresponds to $\mathrm{\Delta }{S}_b\le -1$ 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.