LAUSR

We show that generic linear perturbations ψ solving □gψ+αl2ψ=0 on Reissner–Nordström–AdS black holes have infinite local energy at the Cauchy horizon. Combined with the result of Kehle (2020 Commun. Math. Phys. 376 145–200) that such perturbations ψ remain uniformly bounded and extend continuously across the Cauchy horizon, this settles the linear analog of the strong cosmic censorship conjecture for Reissner–Nordström–AdS: the C 0-formulation is false but the H 1-formulation is true.