# The BTZ black hole violates strong cosmic censorship

## TL;DR

This paper demonstrates that near-extremal BTZ black holes can violate the strong cosmic censorship conjecture due to the smoothness of linear perturbations at the inner horizon, despite the finiteness of the energy-momentum tensor.

## Contribution

It shows that a broad class of theories with near-extremal BTZ black holes violate strong cosmic censorship due to perturbation smoothness.

## Key findings

- Linear perturbations are arbitrarily differentiable at the inner horizon.
- Strong cosmic censorship is violated in a large class of theories.
- Vacuum polarization backreaction does not enforce censorship.

## Abstract

We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker "rough" version of the conjecture is respected. We calculate the renormalized energy-momentum tensor of a scalar field in the Hartle-Hawking state in the BTZ geometry. We show that the result is finite at the inner horizon of a near-extremal black hole. Hence the backreaction of vacuum polarization does not enforce strong cosmic censorship.