Stable Wormholes in Conformal Gravity

Abstract

We present a class of Lorentzian traversable wormholes in conformal gravity, constructed via Weyl rescaling of Minkowski spacetime. As a result, these wormholes are solutions of every theory of gravity that is both conformally invariant and admits Minkowski spacetime as a solution. We specifically examine the case of a wormhole possessing a Morris-Thorne shape function, arising as a solution of a scalar-tensor conformally invariant theory of gravity. We show that these solutions represent regular, traversable wormholes that are also stable at the linear perturbation level. We argue that, when the Weyl symmetry is spontaneously broken, the broken symmetry phase may lead to a stable ``wormhole phase" alternative to the flat ``Minkowski phase".