Exotica ex nihilo: Traversable wormholes & non-singular black holes from the vacuum of quadratic gravity

TL;DR

This paper introduces new traversable wormhole and non-singular black hole solutions within pure quadratic $R^2$ gravity, which do not require exotic matter and are supported solely by the vacuum, especially in the strong coupling limit of General Relativity.

Contribution

The paper presents novel vacuum solutions in quadratic $R^2$ gravity that are traversable and non-singular, arising from singular conformal transformations in the Einstein frame.

Findings

Solutions are supported solely by vacuum without exotic matter.

Solutions arise in the strong coupling limit of General Relativity.

Existence of traversable wormholes and non-singular black holes in pure $R^2$ gravity.

Abstract

We present new traversable wormhole and non-singular black hole solutions in pure, scale-free $R^2$ gravity. These exotic solutions require no null energy condition violating or "exotic" matter and are supported only by the vacuum of the theory. It is well known that $f(R)$ theories of gravity may be recast as dual theories in the Einstein frame. The solutions we present are found when the conformal transformation required to move to the dual frame is singular. For quadratic $R^2$ gravity, the required conformal factor is identically zero for spacetimes with $R=0$. Solutions in this case are argued to arise in the strong coupling limit of General Relativity.