Stability of spherical thin-shell wormholes in scalar-tensor theories

In this article, we construct a family of spherically symmetric thin-shell wormholes within scalar-tensor theories of gravity. In the case of wormholes symmetric across the throat, we study the matter content and analyze the stability of the static configurations under radial perturbations. We apply the formalism to a particular example involving Einstein-Maxwell gravity coupled to a conformally invariant scalar field. We show that stable configurations are possible for suitable values of the parameters involved.

💡 Research Summary

In this paper the authors investigate the construction and stability of spherically symmetric thin‑shell wormholes within the broad class of scalar‑tensor theories of gravity. Starting from a generic Jordan‑frame action that includes a non‑minimally coupled real scalar field ϕ, a self‑interaction potential U(ϕ) and an arbitrary coupling function f(ϕ), they derive the field equations and the corresponding junction conditions for matching two manifolds across a timelike hypersurface Σ. The junction conditions consist of continuity of the metric and the scalar field, together with generalized Israel‑type conditions that involve the jump of the extrinsic curvature and the normal derivative of the scalar field. The presence of the scalar field introduces an extra term Ω, proportional to f′(ϕ) and to the jump of n·∂ϕ, which does not appear in pure General Relativity.

The construction proceeds by taking two copies of a static, spherically symmetric solution described by the line element ds² = –A(r)dt² + A⁻¹(r)dr² + r²dΩ², removing the region r<a from each copy, and gluing the remaining manifolds at the surface r=a. The throat radius a is allowed to depend on the proper time τ of an observer comoving with the shell, enabling a dynamical analysis. By evaluating the first and second fundamental forms on both sides, the authors obtain explicit expressions for the surface energy density σ and the transverse pressure p in terms of the metric function A(r), its derivative, the scalar field and its derivative, and the coupling function f(ϕ).

Focusing on the case of a symmetric throat—i.e., the two spacetimes are identical (A₁=A₂≡A, ϕ₁=ϕ₂≡ϕ)—the junction conditions simplify dramatically. Assuming a constant scalar field on the shell (ϕ′(a)=0) leads to a vanishing jump of the extrinsic curvature trace,