Einstein-Gauss-Bonnet black strings

TL;DR

This paper constructs and analyzes uniform and nonuniform black string solutions in Einstein-Gauss-Bonnet gravity across dimensions five to ten, revealing stability properties and new features in six dimensions, and supports the Gubser-Mitra conjecture.

Contribution

It provides the first comprehensive construction of black strings in Einstein-Gauss-Bonnet gravity for multiple dimensions, including both perturbative and nonperturbative solutions, and explores their stability.

Findings

Stable black strings exist in six dimensions for large Gauss-Bonnet coupling.

Black strings in other dimensions are unstable and thermodynamically unfavorable.

The results support the Gubser-Mitra conjecture linking dynamical and thermodynamic stability.

Abstract

We construct uniform black-string solutions in Einstein-Gauss-Bonnet gravity for all dimensions $d$ between five and ten and discuss their basic properties. Closed form solutions are found by taking the Gauss-Bonnet term as a perturbation from pure Einstein gravity. Nonperturbative solutions are constructed by solving numerically the equations of the model. The Gregory-Laflamme instability of the black strings is explored via linearized perturbation theory. Our results indicate that new qualitative features occur for $d=6$, in which case stable configurations exist for large enough values of the Gauss-Bonnet coupling constant. For other dimensions, the black strings are dynamically unstable and have also a negative specific heat. We argue that this provides an explicit realization of the Gubser-Mitra conjecture, which links local dynamical and thermodynamic stability. Nonuniform black strings in Einstein-Gauss-Bonnet theory are also constructed in six spacetime dimensions.