the presence of higher derivatives, “massive ghosts” also appear (the corresponding classical Hamiltonian is unbounded from below). Nevertheless, there is a possibility that these ghosts could be benign [@Smilga]. For all these reasons, this QG theory has attracted considerable attention in recent years.

In our work, we are interested in *classical solutions to QG in four dimensions*. It can be easily shown that all Einstein spacetimes obey the vacuum field equations of this theory. However, QG also admits additional vacuum solutions with nontrivial Ricci tensor. In this paper, we focus on such *static, spherically symmetric vacuum solutions* without a cosmological constant. They were first studied in the seminal work [@Stelle:1978], in which three families of such spacetimes were identified by using a power expansion of the metric functions around the origin. The failure of the Birkhoff theorem in [Quadratic]{} Gravity has also been pointed out therein. Spherically symmetric solutions were further studied in [@Holdom:2002], where also numbers of free parameters for some of the above-mentioned classes were determined. Recently it has been pointed out in [@LuPerkinsPopeStelle:2015; @LuPerkinsPopeStelle:2015b; @PerkinsPhD] that, apart from the Schwarzschild black hole and other spherical solutions, QG admits a *non-Schwarzschild* spherically symmetric and static black holes.

The 