Strong cosmic censorship: the role of nearly extreme nonrotating black holes

In this paper it is argued that even invoking the dominant energy condition, the Einstein's field equations admit nonglobally hyperbolic, asymptotically de Sitter spacetimes with locally naked singularities and with Cauchy horizons failing to be surfaces of infinite gravitational blueshift; what is more, it is shown the existence of space-time solutions containing Cauchy horizons expected to be stable against small linear nonstationary axisymmetric perturbations in an open set of the physical parameter space where the positive cosmological constant is nearly zero. The price to pay is a violation at ultrahigh densities of Le Chatelier's principle. Given an equation of state, the line of thought introduces black-hole Cauchy horizon instability criteria in terms of the associated adiabatic index, revealing a connection between this subject and the stability theory of relativistic stars. This is used to put forward a tentative, limited formulation of the strong cosmic censorship principle inside black holes (once called dark stars).