Cauchy horizon stability and mass inflation with a cosmological constant

Motivated by the strong cosmic censorship conjecture, we consider the Einstein- Maxwell-scalar field system with a cosmological constant Λ (of any sign), under spherical symmetry, for characteristic initial conditions, with outgoing data prescribed by a (complete) subextremalReissner-Nordstrom black hole event horizon. We study the structure of the future maximal (globally hyperbolic) development, analyze the mass inflation scenarios, identifying, in particular, large choices of parameters for which the Hawking mass remains bounded, and study the existence of regular extensions. We also discuss why our results, although valid for all signs of Λ, only provide evidence for the failure of strong cosmic censorship in the case of a positive cosmological constant.