Wormholes in conformal gravity

TL;DR

This paper introduces a new class of static spherically symmetric wormhole solutions in conformal gravity, showing they can be constructed without exotic matter and may replace black hole singularities with wormholes.

Contribution

It provides a detailed method for constructing wormholes in conformal gravity, demonstrating their existence as exact vacuum solutions and their potential to eliminate black hole singularities.

Findings

Wormholes can be locally conformal to Schwarzschild-(anti) de Sitter spacetimes.

Every conformal gravity theory with static solutions can contain wormholes without exotic matter.

Charged wormhole solutions are explicitly constructed in Weyl and conformal scalar-tensor gravity.

Abstract

We present a new class of solutions for static spherically symmetric wormhole spacetimes in conformal gravity and outline a detailed method for their construction. As an explicit example, we construct a class of traversable and non-traversable wormholes that are locally conformal to Schwarzschild-(anti) de Sitter spacetimes. These wormhole spacetimes are exact vacuum solutions in, but not being limited to, Weyl gravity and conformal scalar-tensor theories. Importantly, the method implies that every conformal theory of gravity with static spherically symmetric solutions will trivially contain wormholes without the need for exotic matter. Applying those results on gravitational theories that possess conformal symmetry in the ultraviolet regime, the central singularities of black holes can be replaced with wormhole throats. We speculate on possible phenomenological consequences. We also discuss the inclusion of matter fields and give explicit examples of charged wormholes in Weyl gravity and conformal scalar-tensor gravity.