Does the Gauss-Bonnet term stabilize wormholes?

TL;DR

This paper investigates how the Gauss-Bonnet term influences the existence and stability of thin-shell wormholes across different symmetries, revealing that it generally shrinks stable parameter regions and affects stability differently depending on symmetry.

Contribution

It provides a detailed analysis of the impact of the Gauss-Bonnet term on wormhole stability across various symmetries, including non-perturbative effects.

Findings

Gauss-Bonnet term shrinks static wormhole parameter space

It does not affect stability of planar symmetric wormholes

Positive small coupling destabilizes spherical, stabilizes hyperbolic wormholes

Abstract

The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary dimensional spherically, planar, and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions which have the Z${}_2$ symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region admitting static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-Bonnet term does not affect their stability. If the coupling constant is positive but small, the Gauss-Bonnet term tends to destabilize spherically symmetric wormholes, while it stabilizes hypebolically symmetric wormholes. The Gauss-Bonnet term can destabilize hypebolically symmetric wormholes as a non-perturbative effect, however, spherically symmetric wormholes cannot be stable.