Instability of black strings in third-order Lovelock theory

TL;DR

This paper demonstrates that homogeneous black strings in third-order Lovelock theory are unstable under s-wave perturbations in nine dimensions, with the instability characteristics depending on the curvature terms in the Lagrangian.

Contribution

It provides the first analysis of black string instability in third-order Lovelock theory, comparing it with general relativity and Gauss-Bonnet theory.

Findings

Black strings in third-order Lovelock theory are unstable under s-wave perturbations.

The critical wavelength for instability increases with curvature power.

Maximum growth rate of instability decreases with higher curvature terms.

Abstract

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension $D=9$, which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet and third-order Lovelock theory. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.