Vacuum and charged asymptotically (A)dS black holes in quadratic gravity

In this paper, we study asymptotic properties of static spherically symmetric black holes in quadratic gravity with a cosmological constant $Λ$. We find that for sufficiently large values of $|Λ|$ these black holes are generically asymptotically (A)dS and form a three-parameter family of black holes, with free parameters being the horizon radius, $Λ$, and Bach parameter $b$. For smaller values of $|Λ|$, fine-tuning of the Bach parameter is necessary to recover asymptotically (A)dS behaviour, resulting in two distinct two-parameter families of spherically symmetric black holes with (A)dS asymptotics. One family is the (A)dS-Schwarzschild solution, the other is a fine-tuned asymtotically (A)dS-Schwarzschild-Bach solution. We also generalise the above solutions to electrically charged black holes, obtaining qualitatively similar asymptotic behaviour. This adds the electric charge as an additional free parameter of these black holes. Both fine-tuned three-parameter families are distinct from Reissner-Nordström black holes.