Three dimensional black strings: instabilities and asymptotic charges

TL;DR

This paper analyzes the stability and asymptotic properties of three-dimensional black strings in Einstein gravity with various forms, revealing their inherent instabilities and characterizing their conserved charges.

Contribution

It introduces a new evolving solution from stationary black strings to singular geometries and characterizes the algebra of conserved charges in this context.

Findings

Stationary black strings are unstable under small perturbations.

New solutions evolve into singularities, indicating instability.

A finite-dimensional symmetry algebra of conserved charges is identified.

Abstract

Three-dimensional Einstein gravity coupled to zero, one and two forms is solved in terms of a polyhomogeneous asymptotic expansion, generalising stationary black string solutions. From first order terms we obtain, in closed form, a new solution evolving from the stationary black string structure to a geometry developing a singularity in the future. This new solution itself may be extended to more general ones. Taking into account subleading terms of the asymptotic expansion, both singularities in the past and the future occur. This demonstrates the unstable character of the stationary black string : tiny perturbations generated by terms breaking the rotational invariance of the stationary black string configurations lead to cosmological-like singularities. The symmetry algebra of the conserved charges also is determined: it is a finite dimensional one. In the general case the surface charge associated to energy is not integrable. However we identify a sub-class of solutions, admitting asymptotic symplectic symmetries and as a consequence conserved charges that appear to be integrable.