Investigations of strong cosmic censorship in 3-dimensional black strings

TL;DR

This paper examines the strong cosmic censorship conjecture in 3-dimensional black strings by analyzing quasinormal modes, revealing that SCC can be violated in these spacetimes and exploring the implications of T-duality on spacetime symmetries.

Contribution

It demonstrates that the SCC conjecture can be violated in 3d black strings and uncovers a new quasinormal mode feature related to the spectral gap at the Cauchy horizon.

Findings

SCC can be violated in asymptotically flat 3d black strings.

T-duality preserves certain spacetime symmetries relevant to SCC.

The spectral gap at the Cauchy horizon is determined by m-frequency modes.

Abstract

Investigating the quasinormal modes of a massive scalar field on the 3-dimensional black string (3dBS), we study the strong cosmic censorship (SCC) conjecture for the 3dBS in the T-dual relationship with the 3-dimensional rotating anti-de-Sitter (BTZ) black hole. It is shown that even though geometries of the two spacetimes are quite different, such as asymptotically AdS for the BTZ black hole and asymptotically flat for the 3dBS, the BTZ black hole and the 3dBS share similar properties for the SCC. Concretely speaking, the SCC conjecture can be violated even for asymptotically flat spacetime, i.e. the 3dBS. These observations lead us to an assumption that the T-dual transformation preserves spacetime symmetries, at least, which are relevant to the SCC. In addition, we find a new feature of the quasinormal mode at the Cauchy horizon: in the case of the 3dBS, the spectral gap, $\alpha_{\mathrm{BS}}$ at the Cauchy horizon is not determined by the `$\omega $-frequency mode', but the `m-frequency mode'.