Novel Cauchy-horizon instability

TL;DR

This paper investigates the stability of horizons in higher-dimensional Einstein-Maxwell-scalar-$\\Lambda$ systems, revealing a new kink instability at the Cauchy horizon that differs from traditional blueshift instabilities.

Contribution

It introduces the concept of kink instability at the Cauchy horizon and analyzes its nonlinear local behavior in static black hole solutions.

Findings

Cauchy horizon is unstable due to kink instability.

Black-hole and cosmological horizons are stable.

Kink instability prevents analytic continuation beyond the Cauchy horizon.

Abstract

The evolution of weak discontinuity is investigated on horizons in the $n$-dimensional static solutions in the Einstein-Maxwell-scalar-$\Lambda$ 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.