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

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