Blowup of the local energy of linear waves at the Reissner-Nordström-AdS Cauchy horizon

Abstract

We show that generic linear perturbations $\psi$ solving ${\square }_g\psi +\frac{\alpha }{l^2}\psi =0$ on Reissner-Nordström-AdS black holes have infinite local energy at the Cauchy horizon. Combined with the result of arXiv:1812.06142 that such perturbations $\psi$ 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.

21 pages, 1 figure

Cited by in corpus (1)

• A New Look at the $C^0$-formulation of the Strong Cosmic Censorship Conjecture