Topological black holes in higher derivative gravity

We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants - the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein's gravity, such black holes require a negative cosmological constant A, in quadratic gravity they can exist for any sign of A and also for A = 0. Different branches of Schwarzschild-Bach-(A)dS or purely Bachian black holes are identified which admit distinct Einstein limits. Depending on the curvature of the transverse space and the value of A, these Einstein limits result in (A)dS-Schwarzschild space times with a transverse space of arbitrary curvature (such as black holes and naked singularities) or in Kundt metrics of the (anti-)Nariai type (i.e., dS(2)xS(2), AdS(2)xH(2), and flat spacetime). In the special case of toroidal black holes with A = 0, we also discuss how the Bach parameter needs to be fine-tuned to ensure that the metric does not blow up near infinity and instead matches asymptotically a Ricci-flat solution.