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) not equal 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.