  The recent discovery of non-Schwarzschild black hole spacetimes has opened
new directions of research in higher-derivative gravitational theories.
However, despite intense analytical and numerical efforts, the link with the
linearized theory is still poorly understood. In this work we address this
point for the Einstein-Weyl Lagrangian, whose weak field limit is characterized
by the standard massless graviton and a spin-2 ghost. We show that the strength
of the Yukawa term at infinity determines the thermal properties of the black
hole and the structure of the singularity near $r=0$. Moreover, inspired by
recent results in the Asymptotic Safety scenario we investigate the
consequences of an imaginary ghost mass. In this case we find a countable set
of solutions all characterized by spatial oscillations of typical wavelength
determined by the mass of the spin-2 field.

General Relativity and Quantum Cosmology;High Energy Physics - Theory