Novel Cauchy-horizon instability

The evolution of weak discontinuity is investigated on horizons in the $n$-dimensional static solutions in the Einstein-Maxwell-scalar-$\mathrm{\Lambda }$ system, including the Reissner-Nordstr"om-(anti) de Sitter black hole. The analysis is essentially local and nonlinear. We find that the Cauchy horizon is unstable, whereas both the black-hole event horizon and the cosmological event horizon are stable. This new instability, the so-called kink instability, of the Cauchy horizon is completely different from the well-known ``infinite-blueshift’’ instability. The kink instability makes the analytic continuation beyond the Cauchy horizon unstable.