Thin-shell wormholes in Einstein and Einstein-Gauss-Bonnet theories of gravity

TL;DR

This paper reviews the stability and existence of thin-shell wormholes in Einstein and Einstein-Gauss-Bonnet gravity, highlighting conditions for their stability across various symmetries and the influence of additional gravitational terms.

Contribution

It provides a comprehensive classification and stability analysis of traversable thin-shell wormholes in different gravitational theories and spacetime symmetries, including the effects of the Gauss-Bonnet term.

Findings

Spherical wormholes are stable against spherically symmetric perturbations.

Certain planar and hyperbolic wormholes with negative cosmological constant are stable.

Stability depends on electric charge, cosmological constant, and spacetime symmetry.

Abstract

We review recent works on the possibility for eternal existence of thin-shell wormholes on Einstein and Einstein-Gauss-Bonnet gravity. We introduce thin-shell wormholes that are categorized into a class of traversable wormhole solutions. After that, we discuss stable thin-shell wormholes with negative-tension branes in Reissner-Nordstr\"om-(anti) de Sitter spacetimes in $d$ dimensional Einstein gravity. Imposing $Z_2$ symmetry, we construct and classify traversable static thin-shell wormholes in spherical, planar and hyperbolic symmetries. It is found that the spherical wormholes are stable against spherically symmetric perturbations. It is also found that some classes of wormholes in planar and hyperbolic symmetries with a negative cosmological constant are stable against perturbations preserving symmetries. In most cases, stable wormholes are found with the appropriate combination of an electric charge and a negative cosmological constant. However, as special cases, there are stable wormholes even with a vanishing cosmological constant in spherical symmetry and with a vanishing electric charge in hyperbolic symmetry. Subsequently, the existence and dynamical stability of traversable thin-shell wormholes with electrically neutral negative-tension branes is discussed in Einstein-Gauss-Bonnet theory of gravitation. We consider radial perturbations against the shell for the solutions, which have the $Z_2$ symmetry. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry.