• black hole dynamics
• General Relativity
• Strong Cosmic Censorship

Strong Cosmic Censorship (SCC) Conjecture is concerned with non-unique extensions of dynamical solutions of Einstein’s Field Equations. A solution, which consists of a Lorentzian manifold and of matter fields, is obtained dynamically if it solves the Cauchy problem formulation of Einstein’s Equations. There are existence and uniqueness results for such Cauchy problem: given suitable initial data, we can identity a maximal solution associated to such data which we refer to as maximal Cauchy development. Such maximal Cauchy developments are often non-uniquely extendible beyond some of their boundary components, which we refer to as Cauchy horizons. SCC states that for generic initial data, the resulting Cauchy development is inextendible. Its validity can be discussed in one of two ways: either one proves metric inextendibility or one tests the stability of the solution. Metric inextendibility can be studied at different regularity levels, the most satisfactory of which is the continuous one. Stability can also be studied at two different levels: either one perturbs the initial data or one studies the propagation of a linear gravitational perturbation.
Reissner-Nordström-Anti de Sitter black holes are dynamical solution of Einstein’s Equations with a Cauchy horizon. We test their stability in the weak and linear regime and prove that the local energy of perturbations at the Cauchy horizon is unbounded, thus pointing in favour of the validity of the conjecture.