We present a new explicit class of black holes in general quadratic gravity with a cosmological constant. These spherically symmetric Schwarzschild–Bach–(anti-)de Sitter geometries, derived under the assumption of constant scalar curvature, form a three-parameter family determined by the black-hole horizon position, the value of the Bach invariant on the horizon, and the cosmological constant. Using a conformal to Kundt metric ansatz, the fourth-order field equations simplify to a compact autonomous system. Its solutions are found as power series, enabling us to directly set the Bach parameter and/or cosmological constant equal to zero. To interpret these spacetimes, we analyze the metric functions. In particular, we demonstrate that for a certain range of positive cosmological constant there are both black-hole and cosmological horizons, with a static region between them. The tidal effects on free test particles and basic thermodynamic quantities are also determined.

• Received 27 June 2018
• Revised 10 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.231104