Dynamical conformal transformation and classical Euclidean wormholes

TL;DR

This paper explores how dynamical conformal transformations can enable Euclidean wormholes in conformally non-invariant gravity models by altering the Ricci tensor's eigenvalues through coupling with scalar fields.

Contribution

It demonstrates that dynamical conformal transformations can induce conditions favorable for Euclidean wormholes in non-invariant gravitational theories.

Findings

Original Ricci tensor eigenvalues are positive, preventing wormholes.

Dynamical conformal transformations couple the Ricci tensor with scalar fields.

Eigenvalues can become negative, allowing wormholes.

Abstract

We investigate the necessary condition for the existence of classical Euclidean wormholes in a conformally non-invariant gravitational model minimally coupled to an scalar field. It is shown that while the original Ricci tensor with positive eigenvalues does not allow the Euclidean wormholes to occur, under dynamical conformal transformations the Ricci tensor, with respect to the original metric, is dynamically coupled with the conformal field and its eigenvalues may become negative allowing the Euclidean wormholes to occur. Therefore, it is conjectured that dynamical conformal transformations may provide us with {\it effective} forms of matter sources leading to Euclidean wormholes in conformally non-invariant systems.