Strong Cosmic Censorship in Horndeski Theory

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