Toward regular black holes in sixth-derivative gravity

We study spherically symmetric static solutions of the most general sixth-derivative gravity using series expansions. Specifically, we prove that the only solutions of the complete theory (i.e., with generic coupling constants) that possess a Frobenius expansion around the origin, $r=0$, are necessarily regular. When restricted to specific branches of theories (i.e., imposing particular constraints on the coupling constants), families of potentially singular solutions emerge. By expanding around $r=r_0\mathrm{\ne }0$, we identify solutions with black hole horizons. Finally, we argue that, unlike in fourth-derivative gravity, the conditions $R=0$ and $g_{tt}{g}_{rr}=-1$ are too restrictive for sixth-derivative gravity solutions.