Yamabe flow, conformal gravity and spacetime foam

TL;DR

This paper demonstrates that a specific solution in conformal Weyl gravity exhibits Yamabe flow, modeling the transition of a wormhole horn to Euclidean space, potentially representing quantum wormholes in spacetime foam.

Contribution

It reveals a novel connection between Yamabe flow and conformal Weyl gravity solutions, suggesting a geometric model for quantum wormhole dynamics.

Findings

Yamabe flow describes the transition from wormhole horn to Euclidean space.

The solution involves a radial electric field in conformal gravity.

Potential implications for quantum wormholes in spacetime foam.

Abstract

It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such transition may describe appearing/disappearing quantum wormholes in a spacetime foam.