We report on several previously overlooked families of static spherically symmetric solutions in quadratic gravity. Our main result concerns the existence of solutions whose leading exponents depend on the ratio $\omega =\alpha /(3\beta )$ of the four-derivative couplings. We demonstrate that the space of models with $\omega >1$ contains a dense set that admits non-Frobenius solutions $(s_{*},2-3s_{*}{)}_0$ (in standard Schwarzschild coordinates), with certain rational numbers $s_{*}(\omega )$. These solutions correspond to a singular core at $\overline{r}=0$. Another related non-Frobenius family, $(s_{*},2-3s_{*}{)}_{\infty }$, exists for a dense set of models with $1/4<\omega <1$, describing a singular boundary at $\overline{r}\to \infty$. Both families are uncovered by recasting the metric into special coordinates in which the solutions become Frobenius. Additionally, for models with real ratios $\omega \ne 1$ we identify six novel families of non-Frobenius solutions around points $\overline{r}={\overline{r}}_0\ne 0$, describing horizons and wormhole throats. Finally, we rederive and summarize all known families of solutions in modified as well as in the standard Schwarzschild coordinates.

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• Alternative gravity theories
• Gravitation