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The strong cosmic censorship hypothesis has recently regained a lot ofattention in charged and rotating black holes immersed in de Sitter space.Although the picture seems to be clearly leaning towards the validity of thehypothesis in Kerr-de Sitter geometries, Reissner-Nordstr\"{o}m-de Sitter blackholes appear to be serious counter-examples. Here, we perform another test tothe hypothesis by using a scalar field perturbation non-minimally coupled tothe Einstein tensor propagating on Reissner-Nordstr\"{o}m-de Sitter spacetimes.Such non-minimal derivative coupling is characteristic of Horndeskiscalar-tensor theories. Although the introduction of higher-order derivativecouplings in the energy-momentum tensor increases the regularity requirementsfor the existence of weak solutions beyond the Cauchy horizon, we are stillable to find a small finite region in the black hole's parameter space wherestrong cosmic censorship is violated.

Strong Cosmic Censorship in Horndeski Theory